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</div><h2>SL Paper 3</h2><div class="specification">
<p>Observer A detects the creation (event 1) and decay (event 2) of a nuclear particle. After creation, the particle moves at a constant speed relative to A. As measured by A, the distance between the events is 15 m and the time between the events is 9.0 × 10<sup>–8</sup> s.</p>
<p>Observer B moves with the particle.</p>
<p>For event 1 and event 2,</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain what is meant by the statement that the spacetime interval is an invariant quantity.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>calculate the spacetime interval.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>determine the time between them according to observer B.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why the observed times are different for A and B.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Rocket A and rocket B are travelling in opposite directions from the Earth along the same straight line.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-12_om_16.33.49.png" alt="M18/4/PHYSI/SP3/ENG/TZ2/03"></p>
<p>In the reference frame of the Earth, the speed of rocket A is 0.75<em>c </em>and the speed of rocket B is 0.50<em>c</em>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, for the reference frame of rocket A, the speed of rocket B according to the Galilean transformation.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, for the reference frame of rocket A, the speed of rocket B according to the Lorentz transformation.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline, with reference to special relativity, which of your calculations in (a) is more likely to be valid.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram shows the motion of the electrons in a metal wire carrying an electric current as seen by an observer X at rest with respect to the wire. The distance between adjacent positive charges is <em>d</em>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-11_om_06.22.52.png" alt="M18/4/PHYSI/SP3/ENG/TZ1/03"></p>
</div>
<div class="specification">
<p>Observer Y is at rest with respect to the electrons.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State whether the field around the wire according to observer X is electric, magnetic or a combination of both.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Discuss the change in <em>d </em>according to observer Y.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce whether the overall field around the wire is electric, magnetic or a combination of both according to observer Y.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Identical twins, A and B, are initially on Earth. Twin A remains on Earth while twin B leaves the Earth at a speed of 0.6<em>c</em> for a return journey to a point three light years from Earth.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the time taken for the journey in the reference frame of twin A as measured on Earth.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the time taken for the journey in the reference frame of twin B.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw, for the reference frame of twin A, a spacetime diagram that represents the worldlines for both twins.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Suggest how the twin paradox arises and how it is resolved.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Muons are created in the upper atmosphere of the Earth at an altitude of 10 km above the surface. The muons travel vertically down at a speed of 0.995<em>c </em>with respect to the Earth. When measured at rest the average lifetime of the muons is 2.1 μs.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, according to Galilean relativity, the time taken for a muon to travel to the ground.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce why only a small fraction of the total number of muons created is expected to be detected at ground level according to Galilean relativity.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, according to the theory of special relativity, the time taken for a muon to reach the ground in the reference frame of the muon.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Discuss how your result in (b)(i) and the outcome of the muon decay experiment support the theory of special relativity.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">This question is about simultaneity.</p>
<p class="p1">Daniela is standing in the middle of a train that is moving at a constant velocity relative to Jaime, who is standing on the platform. At the moment the train passes Jaime, two beams of light, X and Y, are emitted simultaneously from a device held by Daniela. Both beams are reflected by mirrors at the end of the train and then return to Daniela.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2016-09-02_om_16.30.41.png" alt="N14/4/PHYSI/SP3/ENG/TZ0/11"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">State and explain the order of arrival of X and Y at the mirrors according to Jaime.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Outline whether the return of X and Y to Daniela are simultaneous according to Jaime.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A long current-carrying wire is at rest in the reference frame S of the laboratory. A positively charged particle P outside the wire moves with velocity <em>v</em> relative to S. The electrons making up the current in the wire move with the same velocity<em> v</em> relative to S.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by a reference frame.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State and explain whether the force experienced by P is magnetic, electric or both, in reference frame S.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State and explain whether the force experienced by P is magnetic, electric or both, in the rest frame of P.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">This question is about a Galilean transformation and time dilation.</p>
<p class="p1">Ben is in a spaceship that is travelling in a straight-line with constant speed \(v\) as measured by Jill who is in a space station.</p>
<p class="p2" style="text-align: center;"><img src="images/Schermafbeelding_2016-11-10_om_13.51.29.png" alt="N10/4/PHYSI/SP3/ENG/TZ0/D1"></p>
<p class="p1">Ben switches on a light pulse that bounces vertically (as observed by Ben) between two horizontal mirrors \({{\text{M}}_{\text{1}}}\) and \({{\text{M}}_{\text{2}}}\) separated by a distance \(d\). At the instant that the mirrors are opposite Jill, the pulse is just leaving the mirror \({{\text{M}}_{\text{2}}}\). The speed of light in air is \(c\).</p>
</div>
<div class="specification">
<p class="p1">The time for the light pulse to travel from \({{\text{M}}_{\text{2}}}\) to \({{\text{M}}_{\text{1}}}\) as measured by Jill is \(\Delta t\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">On the diagram, sketch the path of the light pulse between \({{\text{M}}_{\text{1}}}\) and \({{\text{M}}_{\text{2}}}\) as observed by Jill.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2016-11-10_om_17.16.38.png" alt="N10/4/PHYSI/SP3/ENG/TZ0/D1.a"></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>State, according to Jill, the distance moved by the spaceship in time \(\Delta t\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Using a Galilean transformation, derive an expression for the length of the path of the light between \({{\text{M}}_{\text{2}}}\) and \({{\text{M}}_{\text{1}}}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">State, according to special relativity, the length of the path of the light between \({{\text{M}}_{\text{1}}}\) and \({{\text{M}}_{\text{1}}}\) as measured by Jill in terms of \(c\) and \(\Delta t\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The time for the pulse to travel from \({{\text{M}}_{\text{2}}}\) to \({{\text{M}}_{\text{1}}}\) as measured by Ben is \(\Delta t'\). Use your answer to (b)(i) and (c) to derive a relationship between <span class="s3">\(\Delta t\) </span>and \(\Delta t'\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">According to a clock at rest with respect to Jill, a clock in the spaceship runs slow by a factor of 2.3. Show that the speed \(v\)<em> </em>of the spaceship is 0.90c.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">This question is about relativistic kinematics.</p>
</div>
<div class="specification">
<p class="p1">A spacecraft is flying in a straight line above a base station at a speed of 0.8<em>c</em>.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2016-08-31_om_10.29.59.png" alt="N15/4/PHYSI/SP3/ENG/TZ0/12.b"></p>
<p class="p1">Suzanne is inside the spacecraft and Juan is on the base station.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
[N/A]
<div class="marks">[[N/A]]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
[N/A]
<div class="marks">[[N/A]]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">While moving away from the base station, Suzanne observes another spacecraft travelling towards her at a speed of 0.8<em>c</em>. Using Galilean transformations, calculate the relative speed of the two spacecraft.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Using the postulates of special relativity, state and explain why Galilean transformations cannot be used in this case to find the relative speeds of the two spacecraft.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Using relativistic kinematics, the relative speeds of the two spacecraft is shown to be 0.976<em>c</em>. Suzanne measures the other spacecraft to have a length of 8.00 m. Calculate the proper length of the other spacecraft.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iv.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Suzanne’s spacecraft is on a journey to a star. According to Juan, the distance from the base station to the star is 11.4 ly. Show that Suzanne measures the time taken for her to travel from the base station to the star to be about 9 years.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p>Muons are unstable particles with a proper lifetime of 2.2 μs. Muons are produced 2.0 km above ground and move downwards at a speed of 0.98<em>c</em> relative to the ground. For this speed \(\gamma \) = 5.0. Discuss, with suitable calculations, how this experiment provides evidence for time dilation.</p>
</div>
<br><hr><br><div class="specification">
<p>An electron is emitted from a nucleus with a speed of 0.975<em>c</em> as observed in a laboratory. The electron is detected at a distance of 0.800m from the emitting nucleus as measured in the laboratory.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For the reference frame of the electron, calculate the distance travelled by the detector.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For the reference frame of the laboratory, calculate the time taken for the electron to reach the detector after its emission from the nucleus.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For the reference frame of the electron, calculate the time between its emission at the nucleus and its detection.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why the answer to (c) represents a proper time interval.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Define<em> proper length.</em></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A charged pion decays spontaneously in a time of 26 ns as measured in the frame of reference in which it is stationary. The pion moves with a velocity of 0.96<em>c</em> relative to the Earth. Calculate the pion’s lifetime as measured by an observer on the Earth.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In the pion reference frame, the Earth moves a distance X before the pion decays. In the Earth reference frame, the pion moves a distance Y before the pion decays. Demonstrate, with calculations, how length contraction applies to this situation.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p>Outline the conclusion from Maxwell’s work on electromagnetism that led to one of the postulates of special relativity.</p>
</div>
<br><hr><br><div class="specification">
<p>One of the postulates of special relativity states that the laws of physics are the same in all inertial frames of reference.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by inertial in this context.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>An observer is travelling at velocity <em>v</em> towards a light source. Determine the value the observer would measure for the speed of light emitted by the source according to</p>
<p>(i) Maxwell’s theory.</p>
<p>(ii) Galilean transformation.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">This question is about relativistic kinematics.</p>
<p class="p1">The diagram shows a spaceship as it moves past Earth on its way to a planet P. The planet is at rest relative to Earth.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2016-09-11_om_10.50.39.png" alt="M14/4/PHYSI/SP3/ENG/TZ2/10"></p>
<p class="p1">The distance between the Earth and planet P is 12 ly as measured by observers on Earth. The spaceship moves with speed 0.60c relative to Earth.</p>
<p class="p1">Consider two events:</p>
<p class="p1"> Event 1: when the spaceship is above Earth</p>
<p class="p1"> Event 2: when the spaceship is above planet P</p>
<p class="p1">Judy is in the spaceship and Peter is at rest on Earth.</p>
</div>
<div class="specification">
<p class="p1">Judy considers herself to be at rest. According to Judy, the Earth and planet P are moving to the left.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">State the reason why the time interval between event 1 and event 2 is a proper time interval as measured by Judy.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) Calculate the time interval between event 1 and event 2 according to Peter.</p>
<p class="p1">(ii) Calculate the time interval between event 1 and event 2 according to Judy.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) Calculate, according to Judy, the distance separating the Earth and planet P.</p>
<p class="p1">(ii) Using your answers to (b)(ii) and (c)(i), determine the speed of planet P relative to the spaceship.</p>
<p class="p1">(iii) Comment on your answer to (c)(ii).</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Determine, according to Judy in the spaceship, which signal is emitted first.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">This question is about a light clock.</p>
</div>
<div class="question">
<p class="p1">One of the postulates of special relativity refers to the speed of light. State the other postulate of special relativity.</p>
</div>
<br><hr><br><div class="specification">
<p>This question is about relativistic kinematics.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>An observer at rest relative to Earth observes two spaceships. Each spaceship is moving with a speed of 0.85 <em>c</em> but in opposite directions. The observer measures the rate of increase of distance between the spaceships to be 1.7 <em>c</em>. Outline whether this observation contravenes the theory of special relativity.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The observer on Earth in (a) watches one spaceship as it travels to a distant star at a speed of 0.85 <em>c</em>. According to observers on the spaceship, this journey takes 8.0 years.</p>
<p>(i) Calculate, according to the observer on Earth, the time taken for the journey to the star.</p>
<p>(ii) Calculate, according to the observer on Earth, the distance from Earth to the star.</p>
<p>(iii) At the instant when the spaceship passes the star, the observer on the spaceship sends a radio message to Earth. The spaceship continues to move at a speed of 0.85 <em>c</em>. Determine, according to the spaceship observer, the time taken for the message to arrive on Earth.</p>
<div class="marks">[8]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State <strong>one</strong> prediction of Maxwell’s theory of electromagnetism that is consistent with special relativity.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A current is established in a long straight wire that is at rest in a laboratory.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>A proton is at rest relative to the laboratory and the wire.</p>
<p>Observer X is at rest in the laboratory. Observer Y moves to the right with constant speed relative to the laboratory. Compare and contrast how observer X and observer Y account for any non-gravitational forces on the proton.</p>
<p> </p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p>Two protons are moving with the same velocity in a particle accelerator.<br><img 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" alt><br>Observer X is at rest relative to the accelerator. Observer Y is at rest relative to the protons.</p>
<p>Explain the nature of the force between the protons as observed by observer X <strong>and</strong> observer Y.</p>
</div>
<br><hr><br><div class="specification">
<p>This question is about simultaneity.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the postulate of special relativity that is related to the speed of light.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A rocket moving at a relativistic speed passes an observer who is at rest on the ground equidistant from two trees L and R. At the moment that an observer in the rocket is opposite the ground observer, lightning strikes L and R at the same time according to the<br>ground observer. Light from the strikes reaches the observer in the rocket as well as the observer on the ground.</p>
<p style="text-align: center;"><img 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" alt></p>
<p style="text-align: left;">(i) Explain why, according to the observer in the rocket, light from the two strikes will reach the ground observer at the same time.</p>
<p style="text-align: left;">(ii) Using your answer to (a) and (b)(i), outline why, according to the rocket observer, tree R was hit by lightning before tree L.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A train is passing through a tunnel of proper length 80 m. The proper length of the train is 100 m. According to an observer at rest relative to the tunnel, when the front of the train coincides with one end of the tunnel, the rear of the train coincides with the other end of the tunnel.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain what is meant by proper length.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw a spacetime diagram for this situation according to an observer at rest relative to the tunnel.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the velocity of the train, according to an observer at rest relative to the tunnel, at which the train fits the tunnel.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For an observer on the train, it is the tunnel that is moving and therefore will appear length contracted. This seems to contradict the observation made by the observer at rest to the tunnel, creating a paradox. Explain how this paradox is resolved. You may refer to your spacetime diagram in (b).</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>This question is about time dilation.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Two space stations X and Y are at rest relative to each other. The separation of X and Y as measured in their frame of reference is 1.80×10<sup>11</sup>m.</p>
<p><img 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" alt></p>
<p>State what is meant by a frame of reference.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A radio signal is sent to both space stations in (a) from a point midway between them. On receipt of the signal a clock in X and a clock in Y are each set to read zero. A spaceship S travels between X and Y at a speed of 0.750c as measured by X and Y. In the frame of reference of S, station X passes S at the instant that X’s clock is set to zero. A clock in S is also set to zero at this instant.</p>
<p>(i) Calculate the time interval, as measured by the clock in X, that it takes S to travel from X to Y.</p>
<p>(ii) Calculate the time interval, as measured by the clock in S, that it takes S to travel from X to Y.</p>
<p>(iii) Explain whether the clock in X <strong>or</strong> the clock in S measures the proper time.</p>
<p>(iv) Explain why, according to S, the setting of the clock in X and the setting of the clock in Y does not occur simultaneously.</p>
<div class="marks">[9]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Two rockets, A and B, are moving towards each other on the same path. From the frame of reference of the Earth, an observer measures the speed of A to be 0.6<em>c</em> and the speed of B to be 0.4<em>c</em>. According to the observer on Earth, the distance between A and B is 6.0 x 10<sup>8</sup> m.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Define frame of reference.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, according to the observer on Earth, the time taken for A and B to meet.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Identify the terms in the formula.</p>
<p style="text-align: center;"><em>u′</em> = \(\frac{{u - v}}{{1 - \frac{{uv}}{{{c^2}}}}}\)</p>
<p> </p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine, according to an observer in A, the velocity of B.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine, according to an observer in A, the time taken for B to meet A.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce, without further calculation, how the time taken for A to meet B, according to an observer in B, compares with the time taken for the same event according to an observer in A.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>This question is about relativity.</p>
<p>Carrie is in a spaceship that is travelling towards a star in a straight-line at constant velocity as observed by Peter. Peter is at rest relative to the star.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Carrie measures her spaceship to have a length of 100m. Peter measures Carrie’s spaceship to have a length of 91m.</p>
<p><img 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" alt></p>
<p>(i) Explain why Carrie measures the proper length of the spaceship.</p>
<p>(ii) Show that Carrie travels at a speed of approximately 0.4 c relative to Peter.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>According to Carrie, it takes the star ten years to reach her. Using your answer to (a)(ii), calculate the distance to the star as measured by Peter.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>According to Peter, as Carrie passes the star she sends a radio signal. Determine the time, as measured by Carrie, for the message to reach Peter.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>This question is about relativistic kinematics.</p>
<p>A source of light S and a detector of light D are placed on opposite walls of a box as shown in the diagram.</p>
<p><img 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" alt></p>
<p>According to an observer in the box the distance <em>L</em> between S and D is 6.0m. The box moves with speed <em>v</em>= 0.80c relative to the ground.</p>
<p>Consider the following events.</p>
<p style="padding-left: 30px;">Event 1: a photon is emitted by S towards D<br>Event 2: the photon arrives at D</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In the context of the theory of relativity, state what is meant by an event.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) Calculate the time interval <em>t</em> between event 1 and event 2 according to an observer in the box.</p>
<p>(ii) According to an observer on the ground the time interval between event 1 and event 2 is <em>T</em>. One student claims that \(T = \frac{t}{{\sqrt {1 - \frac{{{v^2}}}{{{c^2}}}} }}\) and another that \(T = t\sqrt {1 - \frac{{{v^2}}}{{{c^2}}}} \).</p>
<p>Explain why both students are wrong.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Relative to an observer on the <strong>ground</strong>,</p>
<p>(i) calculate the distance between S and D.</p>
<p>(ii) state the speed of the photon leaving S.</p>
<p>(iii) state an expression for the distance travelled by detector D in the time interval <em>T</em> (<em>T</em> is the interval in (b)(ii)).</p>
<p>(iv) determine <em>T</em>, using your answers to (c)(i), (ii) and (iii).</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>This question is about length contraction and simultaneity.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Define <em>proper length</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A spaceship is travelling to the right at speed 0.75 c, through a tunnel which is open at both ends. Observer A is standing at the centre of one side of the tunnel. Observer A, for whom the tunnel is at rest, measures the length of the tunnel to be 240 m and the length of the spaceship to be 200 m. The diagram below shows this situation from the perspective of observer A.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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" alt></p>
<p style="text-align: left;">Observer B, for whom the spaceship is stationary, is standing at the centre of the spaceship.</p>
<p style="text-align: left;">(i) Calculate the Lorentz factor, γ, for this situation.</p>
<p style="text-align: left;">(ii) Calculate the length of the tunnel according to observer B.</p>
<p style="text-align: left;">(iii) Calculate the length of the spaceship according to observer B.</p>
<p style="text-align: left;">(iv) According to observer A, the spaceship is completely inside the tunnel for a short time. State and explain whether or not, according to observer B, the spaceship is ever completely inside the tunnel.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Two sources of light are located at each end of the tunnel. The diagram below shows this situation from the perspective of observer A.</p>
<p style="text-align: center;"><img 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" alt></p>
<p style="text-align: left;">According to observer A, at the instant when observer B passes observer A, the two sources of light emit a flash. Observer A sees the two flashes simultaneously. Discuss whether or not observer B sees the two flashes simultaneously.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A spaceship S leaves the Earth with a speed <em>v </em>= 0.80<em>c</em>. The spacetime diagram for the Earth is shown. A clock on the Earth and a clock on the spaceship are synchronized at the origin of the spacetime diagram.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the angle between the worldline of S and the worldline of the Earth.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw, on the diagram, the <em>x′</em>-axis for the reference frame of S.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>An event Z is shown on the diagram. Label the co-ordinates of this event in the reference frame of S.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>An observer on Earth watches rocket A travel away from Earth at a speed of 0.80<em>c</em>. The spacetime diagram shows the worldline of rocket A in the frame of reference of the Earth observer who is at rest at <em>x </em>= 0.</p>
<p style="text-align: left;"><img 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"></p>
<p>Another rocket, B, departs from the same location as A but later than A at <em>ct </em>= 1.2 km according to the Earth observer. Rocket B travels at a constant speed of 0.60<em>c </em>in the opposite direction to A according to the Earth observer.</p>
</div>
<div class="specification">
<p>Rocket A and rocket B both emit a flash of light that are received simultaneously by the Earth observer. Rocket A emits the flash of light at a time coordinate <em>ct </em>= 1.8 km according to the Earth observer.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw on the spacetime diagram the worldline of B according to the Earth observer and label it B.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce, showing your working on the spacetime diagram, the value of <em>ct </em>according to the Earth observer at which the rocket B emitted its flash of light.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain whether or not the arrival times of the two flashes in the Earth frame are simultaneous events in the frame of rocket A.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the velocity of rocket B relative to rocket A.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A rocket of proper length 450 m is approaching a space station whose proper length is 9.0 km. The speed of the rocket relative to the space station is 0.80<em>c</em>.</p>
<p style="text-align: center;"><img 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"></p>
<p>X is an observer at rest in the space station.</p>
<p> </p>
</div>
<div class="specification">
<p>Two lamps at opposite ends of the space station turn on at the same time according to X. Using a Lorentz transformation, determine, according to an observer at rest in the rocket,</p>
</div>
<div class="specification">
<p>The rocket carries a different lamp. Event 1 is the flash of the rocket’s lamp occurring at the origin of <strong>both</strong> reference frames. Event 2 is the flash of the rocket’s lamp at time<em> ct'</em> = 1.0 m according to the rocket. The coordinates for event 2 for observers in the space station are <em>x</em> and <em>ct</em>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-09-27_om_07.57.21.png" alt="M17/4/PHYSI/SP3/ENG/TZ2/05c"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the length of the rocket according to X.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A space shuttle is released from the rocket. The shuttle moves with speed 0.20<em>c</em> <strong>to the right</strong> according to X. Calculate the <strong>velocity</strong> of the shuttle relative to the rocket.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the time interval between the lamps turning on.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>which lamp turns on first.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On the diagram label the coordinates <em>x</em> and <em>ct</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State and explain whether the <em>ct</em> coordinate in (c)(i) is less than, equal to <strong>or </strong>greater than 1.0 m.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the value of <em>c</em> <sup>2</sup><em>t </em><sup>2</sup> – <em>x </em><sup>2</sup>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>An electron X is moving parallel to a current-carrying wire. The positive ions and the wire are fixed in the reference frame of the laboratory. The drift speed of the free electrons in the wire is the same as the speed of the external electron X.</p>
<p style="text-align: center;"><img 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W6DxVPFX8WcgcdK7969zR/fueYnTGgXX3yxucQC7vnnn28E2uDBg80mNn9a/3fyueeee4xbJgKQaXnQx92fnnsjRowwfODKybNBXvzp2UwDD5hYfvzjHxvfdsxL+M0ziPiJfK677jrDC3WlTpiJIJ4hZETwGf/zSb/j9cTgq8I+KWJr0/HOE+LEBdEOvCPFSAV9MVQyusbo7verzoiNXBaLyyGuiAiUNITwIw88dvCQ4Y/vXCsmYBGseLssX77caL94sCCYrWsjz4wZM6bw7HnnnSd4QHz96183s4J3333XuGnStkFCyDOwUy/4YLPVpEmT5MQTTwwmNb8ZBPDeQUizuWb99deXY445xkSbDD4AX+Tz5JNPmnzJv7m52XjsWGEffCbNbwZfK+xpK6VkCNAviq2tJHu6dSps87hpFiMV9MVQyegavtk77bRTRqXnt1hMNs8884wRhmnd+RCkvBB9+vQxbocIbr5zjXtBIoQA4RJwlyQtA/H3vvc9uf32242mTugEtHaEO/7luEVyn3SYl2hPpuaXXHJJMGu5+eabZc899zRpyJvFUnj5+OOPhb0UfkI4EyqBP3ghbz5xE8WFMjhIMXi99957Jj/yJX94obygK6a/nDTfrbAn8qX14U+TXyM8yztvXXFd1Je+VkypUEHvAl1HedBAvJRKrRFgOorgbGpqan2jjF9/+ctfBPs0hIDmD+Ia9/yExs1uVNrEpuWTwQahyYatE044wWj3xLIhXDH5cN+mJz80tt/97nf+rM33q6++2mjb/Aim//Of/9wqPR5CeGMhsG1aPvnNrMB6+diHMMuwYziYN149hFOoFCHsGehoMxX28Siz0cnlO7/pppsWLVQFfVFYsrnItEsXYltjj7DAhS+tycaf64oVKwo/rQnGf61w0/fFprOfvltmR6N1w8TEA/nTMSMpRthU/ffsM/Cy8cYbr/OI5dGms5+2TP8DhGIIprf3CeNcSWLwIT6OCvt4lHFRdfnO77XXXibIWbBkFfRBRPR3bhBgJyfCwgbycsEY2i9B0CArKPnOteBCOOYcBLidCtv0eJcQGqFnz56tWOIlw3RjhbdNj2381FNPbZWWH5hhbFwjm5ZnqXNw5yqauN/f3qZH0+eP+5hrmFVABC+jTkFeZs+ebbxt1mHG8QW/sEeYKa2LQNDctm4Kd1f0hCl3WKbKCTMB9jWltQggNDF7uJza4oKIkMZDxK6HEOb1q1/9alFXQyI9Hn744ebkKswSCFts0JhGgpoYvJ5++ukmFDCDE2YfBgkEPeUFiYVbZiqff/652UiFBo5wZgAIbp5hwLn11luNxw0LqzYIG+6mBLRCaGDfx977j3/8wwwULAgTfgETDgu3bNJipnD22WcHWanIbyvsCTyHsNcwx61hxtxWbnyb1jnF/1KNPh6jqqRAew2zr1WFgZwVYo8FjAtYVirbCEzO4ETIIlj5w77ONWt+8eeJ8EaY7rbbbiYYGoMOcevxQS9G2M2JX4PphGBjBJxiIZnZQZAoD+0dO781s1x11VXGBh9My2+0fMrGO4e8cd9kwOE6gw73JkyYUHgUWzz5QeRPOWH1LDzk+AvC3gZDU83eMbhFsiPuEQP6OlRsF5Veqz4CnBYzdOjQ6hecwxLtyUbl7rYM7u5kJ+oPf/hDJ7sP08I1atQoj7+8UhA7V3wSE4fYOM8884zGx1kDaiXe+bA8VaNfZ+jTC1kjwFQfbRVt0AWxmej+++/P/OAMzD6//e1vzV817bNRGGLTt3b9qHRp7+GJhGbP4e1Ev7RrB2nz1eeTIaA2+mQ4aaoqIZA0xnwp7LDDlZN4MMNYwnZut4uzqOq/x9oAbpLWlINQ5uASpsQsepI+aJ+3+fKJQGejErZ38rGhj3kGdzrI5s13FmT/+te/yoYbbmgWnouZecxDa4KU4XqJfZcAaZiU/HnZdPaTtZ+nn37a/MQMZnnhgrXrb7DBBoUFZ/tcJT4R9iwSY8JB2GswNPcoYwIuRqrRF0NFr2WCAN4sLEbuvffezsv3C3I8Vg466CD5/e9/b/74br1YELp4z3BqD4SgxM7OTlQE5q9//WuzcSvM3sxOWsI0cDYrwozdqcTNsRo8QtwKcq6ddtppctJJJ5m0RB4kIidx6osRvHAmLaEM4IUBjN9chxhgbDn8/tWvfmXyo56cW0s5HMJiiQGC3+zsrSaxKAtGqtm7R51Tz+i/QdIwxUFEMvxdSojYDNmsWNFPPPGEOQA77QJsFI4I4p/85CdmNykaJoQZAdMOB3LgBcNhIwhR4sAgiAlj4D94hPgkuDLiqujXphG07Dz1H/ZB/njpcG7sRRdd1Ao7Qhqwo5YNRpYXBjsGiWIHlROvBpOWfyclMxMOQWGQgHc8gxCgXGcAw4PHmsCoJ144xQ4qt4xFYWfTuPpksARLfO4tj67yroV8GJRZSGdB3hXRD6D+/fu3ylI1+lZw6I+sECDGPCaEtEI+jv+77rqrEEoBDxkIIYvLIvcQ3HiuIOQR3AhNK+RtegQtboqYc/zEQIWGbYWWTY+GZQOk+dPjuolLJOXbtDyLxktoBT8huDldygp5m56ZCh44+NLjOkp+EM+zL8DPC+UwEHGSVh6o0SNf0tfCZoau20cFvWtEU+RHx0e4NBohpBBkCKFKE7tI7SHblGUFJteCO0zhKyhYbXp81NH0/YSGxmDlz5fvYSGVmV3479m8CfXwzjvv+LM239u2Xf262nT209YHE4wdUHjeXrfpyIRdsVbrW6eADC4wsDMTaeTIl35zW9omIIxH8Cxj8lRBnxZZh88zNUe4NBJhTsBPnU09fqFXKQzYJLV48eJC9tY2zzW7gcreRFtmUZUFLpvOfrIJKpi+c+fOhcO+bTryok2LnYbFArFfoNtnWPTFnOEnsGEBFrxsOj75TbTI4KYyQt9iFoFser6zmYo9BHkiGwwNYd9okS/ZMBWMU5S2bYq9R2qjT4uqw+ex1yJcgi+5wyJyl1XcsYDlMBxlZ2bhEs8ZdiHbBVpmE+wu5YWzC6W2XMwrEydONPZuXiAEK14vCKdgFEg0s8MOO8yYdZidYSpByGNGwRwUDGvAwi8hkImOaQU1u3SZzgft//DDwinCkM1a8MIAxCLr8ccfL0TZ9BMzQ8xR7LC19SQcMguzxez/9tko7GyaSn0S18hGKQXfRiDXR4fSfvQL/9qRwdHVhgjNJz0CkydP9u644470GdVIDkmOBSynKnGbfthUcsABB5jj90jLd66F0d13320O/CYtf1dccUVh89XPfvYzb8aMGYVHOYaQw8RtWg4K55DuMOIoPntAOc8MGTLECzt4nOPmONzb5s3nrbfeGpa1yYf8bHrqSXmWOE4wWBZpsyS7WW7hwoVZslG1sl2+8/S93XffvSjv2bZqUZYa9yLChhezEYidkpw12tLS4ry61RJWvFhbbbWV169fP+d1GDFiRKsBJGkBDDr9+/ePTW5532GHHVqlrRZ2rQoN/GgkYR+2kzUASaKf7DoO212vppsczQ+Z+tsp+TpTrxzx6YIVDumAgsG7XORtzQ/s+GRxNGiOcVGGzYPNVVtttVXiMpLwZM1LmGiIZVMKYQpisZU1BGuyCXsecxXeRf71A4td2DPVuo6bKWYqFsMxg9Ur2Xfe85h4pSNMv5zbEHStNLkmGio0UdUQQKOfM2dO1crLoiC0eLR5tPpKEFopZo7tttvO23777QtmlmBZaLX8JaWgmSPqOcoPpo/iibTct0Qf8P+21+1nmKmJZ4L9p5R65kGjt3VEsyc+jt/cZO/V06erd/6II44INUGq1026QdT50zbaofOMc5Ihi5l2wY3FykoRM6Jzzz1XRo4cuc7CFIuveDjhzskfvudcCyMWZNF00Zb5ZAEtzCUObZxNVszMSI/7oD0WsBhPuFiyCQqtmnAJHPhNHoQqCM7qKBMPGnggEiWf7H7188IzNswB+eBLzy5U6kmdq+W3HYZlKdfZA9AIkS/ZTMc7kYZoaxbbw2ZxarpJg24FnqXBmHq53C1XATbLzpIdpcR8wf2vUoQADJsKg29arxuEJXFp2MHqJwQuAzXhpoNeNzfddNM6oY2Led0w4GDW4sUPxtPhUHJ22Qa9bhCGDGh+wuuGjV4IEfvyWw+gvHrd+Pn3f0c5YOMam9Twua+kguAvt1rfXbzzd955pyxZssTsei7Gt2r0xVDJ8Br2ZISgtWFnyIrzoisVY74URgk7MHDgQCP87EYiBCHXuBckToYilAAaOukRMghQfN2DswDcLu19PkmP2yTuk9dee20wazMzIMgXafy8EG+eXbZ+QhgQA+eII44o8AJPhE/genCjHS6d3bt3Lwh5ywvlBd1C/eXk8TtY1nPkS955bOtp3nnWZaLcslXQ57BnDxo0SDg/tp4I314CliEkeXGzIvzUOZ3JkhWwXOOenxDkmD6skOeeTY8wDqbHD58X1p+O7whyZjJB4sBwu/PW/wzXgi89+DETsQOITc9vdtIGN9qxP8Fq8pZnnuEkrRtuuCHISu5/U08GqXoNhsbGqXLfedtXbHsXa0wV9MVQyfgaoWcJZxvUGDNmK1XxlTgWsByG8MIhNowlu2uUazZ8gb2HgGZ3KaYDm85+cmA5p/n4Cfs402fIpuM7QroYsYEK7xJL9hl2h2K3D5JNa9PZT3997DN4Alkt36bj3ieffFLcK8M+mPNPTGL1KOzTvPOEvog7klAFfQ47NgJj1KhRBe0xhyyWxBImG+LIVDpgWRKm2EWK/dsvvO0CMff8hI0ck4FdwLQCE+FP6AJeTj+hcXIebVAgE39k9OjR/qTm+ymnnGJs7n5eeJbyggeVo62xOGkHf8sLvzm2MKjNYS7Cnu/nhXIYcFkkrmWywt6PdS3XB97tO19qyGhcUKE4N2VdjM1xD8EDg8W9on6xOebbzxqChtC42JJtJEX//Up8j1qMpTyE5O23324iTfKbcANgbU0cfl93tGK8aLCR77DDDvLee+8JW/URMn7hag8rYREd75YjjzzSCGAOFOGAEEIg8DIHiZDJ2PYxBTEYYg7Cvz0YLgHTD+Vjh8X8QogAvCz4IwxCsb0CeAshOIjJw2wF3/pjjz22UM8gL/yOw67YM1ld45Ca1157zWBSrb5V6bqW8s7TN1EuiLrq74vFeFRBXwyVnFyzq/HYVONG7JywvA4brmLMr5NxxIUkwgpsrWcTnhxWUPLyEGANmzAzEUvYQYlWSURIPFn8Qpu8sJ/bDU7kwelVmFSIJGjdHW1ewU+0cmvvZ5AIettMmjTJLBbjWYGmTnhkeMF0FHfCFLzYU60Q+LECIcJjKch3Hn4z6NKODID1IOyTvvN4eKEk0BdxJIiletp4UI91YSMN8SumTp1ac9V77bXXzIaXajOedtMPh3c/9NBDJbFdbsiCJIWwCerwww9fZwNWkmdLTZMWu1LLc5GeuDiVCqfhgr9S82AzXNQ7zwY4NlnddNNNibNWjT52KMw+AaM8pwKhjeFeR0zxOM0sa66zMNnYOifR6G1a/WyNQK1iV2+RL4u987QU6z2EOuCoy1JMuiroW/fzXP/CfIALVqkLNrmulDKnCCgCiRDAswbzG+tdQfNeXAYq6OMQ0vslI1CJGPNJmaBsqJI7b5PyUovp8MfnIBicAFinqDViJoknij0/t9b4rxS/6l5ZKWQbNF8EBYuL1TgWsBjETOH9m5CKpdFr4Qiwd4BQAxw4XovEgiwLsyzQWrfYWqyHa55V0LtGtIHzw0+7mscCBqG2PuP14H0RrFs1f++8887GbZH2rEWywp5NbSrsV7egCvpa7Mk55ZkgXexa5OzULIiZRKMcQVdJfNHqCeWAn3qtEsK+ESJfJm0fFfRJkdJ0kQiwbZ8do9hGsyLKV7ONG/TZS4Bvf1j4BjelVDYX1hissMeRoVZnKC5QUkHvAsUGz4MXqBox5qNgZqBh96eabaJQSn6PQG648LLztJbJCvulS5eaUMeNKuxV0NdyL84J7yx8MdUnil8Sk5gAACAASURBVGJWhN+xmm3cok9gNWZJdu3Dbe7Vyw1hX8+RL5MgqYI+CUqaJhQBNGnirWRpsoE5BBKxYJTcIYBWj7An5EI9kA2GxiEmjabZq6Cvhx6cUR2w32Ky4Ri8LH2uGWxwCUQwKblFgMETl9lgvHu3pVQvNyvs6ynyZRL0VNAnQUnTFEUgLzHmMdtk5elTFJg6usgAzsLs3Llz66ZWCHtmKmysqnWzVNJGUUGfFClN1wqBPBwLCENMwTHb2JOdWjGpP5wgwCDKYiab0eqFOBsBc2OjCHsV9PXSc6tYD0w2eTgWkCqzPqBmm8o3PiElbHiJypdWnRJYvLfCHvNfPZMK+npu3QrV7emnnzaud2ysyZrUbFOdFkAorr/++nWl1YOcFfacxlVPM5Zgr1BBH0REf0ciYHdL5iFomJptIpvK+c2ePXuaGDL15rGCsCciJG7C9SrsVdA7fx3qN0MWrjDZ7L333rmoJGYbdsKqt011moMZHH+1GvAsCiUbH6dehb0K+qjW13utEHjuueeMB0Zedp9itrFHALZiVH9UDIFaD3gWBYxf2NdbMDQV9FEtr/cKCFiTDd4KeSA122TTCmj0zKIIYFePZIV9vUW+VEFfj73VcZ3YLEPMk/33399xzuVnZ+POZ7lRq3zua/tJfNCJFFrLAc+iWgBhb4Oh1Ytmr4I+qsX1nvFTzzLGfFgT4MevZpswdCp7nTURjrSr9YBnUSihQFhhXw+RL1XQR7W23jMxyfFTz9POUzRJpta6SSq7DooJj41q9RIaoRiSVtjXQ+RLFfTFWlivGQR4ibM8FjCsGay3jZptwhCq/HWwx4RTT6ERiqFGPesh8qUK+mKtq9cKJht2DubNfRGzTadOnbSVMkag3gKeRcFpg6HVauRLFfRRrdvA9/An5lhANpPkiTDbMJXOMvZ9nvDIkhe0XRSBWbNmZclG1cq2wr4WI1+qoK9aN6mdgvISY74YYtiF9bjAYshkcw1FYMWKFXW7ozSIaq1GvlRBH2zJBv+Nf3rWxwJGNYF620Shk829egx4FoVkLUa+VEEf1aINeC8PxwKGwU4IhuXLl6vZJgygjK6j1eOZZTfVZcRGVYulzrUU+VIFfVW7R74LQ1vGbZEOnEdSs00eW2U1T/UcGiEMdSvsayHypQr6sFZssOt5ijEfBj27Yb/+9a+H3dbrGSJQzwHPomBF2NdC5EsV9FGt2ED38nIsYBjk9sg3BIpSPhHYbbfdzG7Zeg2NEIa6jY+T58iXKujDWq+BrmOywWUxLwHLikGP2QbtSSm/CCDw8Iiq59AIYej7hX0e4+OooA9ruQa5bmPM9+rVS/K809QGMWuQZqnZatZ7wLOohrHCPo+RL1XQR7VcA9wjxjwvJ500r2TP88wzj3nFrtp8sYt61113NQfUVLvsPJRHH7XB0PKk2augz0PvyIgH6w6XZ5MN0HDAiJptMuokZRRLaATiEdVzwLMoWJgZW2Gfl8iXKuijWqyO71mTTV6OBYyCWt0qo9DJ3z0EXSMEPItC3gr7vES+VEEf1Vp1fC9vxwKGQY3ZZoMNNsi1aSmM90a+jlaPkGtUrZ62R9jnJfKlCvoGfBtfeeUVIzzzbrKhaTDb1AKfDdiNIquMkCM0AofWNDrZYGhZRr5UQd9gvTCvMebDmgGzjR4wEoZOvq/bdRU8phqdrLDPKvKlCvoG6oEELMvjsYBhTYCAIIZK3uLhh/Gr19dFAAHHDJK+1+iUZeRLFfQN1PvwssnbsYBR8GO2ydMRhlG86r3iCHBuAH3ujTfeKJ6gwa5ihrTB0Oxu72pAoIK+GijnoAwWNTkWcN99980BN/EsoAGq2SYep1pI0YgBz6LaBZOWFfZ2j0hUehf3VNC7QDHneeQ9xnwx+PDD5oQrNdsUQ6e2rhGfiHUW1erXtpsV9tWKfKmCfi32dfstzzHmw0DHbNO9e/ew23q9xhCwu2UbLeBZVDMh7KsV+VIFfVRL1ME9poZox3mNMV8MYjXbFEOltq8xM+vSpUtDBjyLajkbH6fSkS9V0Ee1Qo3fq0WTDZAzMBEFEV9spfpBgN2yrLuoVt+6Tf3CvlLxcVTQt8a8rn5x9itaFJ4PtURvvvmmbL311rXEsvKaAAG0eoQ9Zx8otUbACvtKRb5UQd8a77r5VQsx5ouBjbaHRq+bpIqhU/vXCI3Apr1GDo0Q1oqVjHypgj4M9Rq+jrCcM2eOfPvb364584eabWq44yVgHXNcowc8i4IJfCoR+VIFfRTqNXov78cCRsHKTETNNlEI1f49Ng0R8ExDIxRvSyvsXUa+VEFfHOuavYqgXL58eU0GAmMmQudWs03Ndr/EjBPwjNAISsURQNi7jHypgr44zjV5lS3VaPPEmKej1Bqp2abWWqx8fjXgWTLsbDC0tJEvVdAnw7smUtVKjPkwMNVsE4ZMfV5nDQn/cdyAlcIRsMI+TeRLFfTh+NbUnVo5FjAMVGYjmG1qzRU0rD56PR4BQiPwp6ER4rFKG/lSBX08xrlPgZB87bXXjMkm98yGMKjHBYYAU+eXNeBZ8gZOE/lSBX1ynHOZkmnvU089JcQSwQ+3VgkPDPW2qdXWK59vNHp2QdsZafk5NcaTNhjatGnTpJTIlyroa7x/1FqM+WJwMyPBU0jNNsXQqf9r+NW/+uqrGhohYVNbYV9K5EsV9AnBzWOyWjsWMAxDzDaEalBqTAQ04Fnp7V5q5EsV9KVjnIsnMNnU0rGAUaBhtmH6rtS4COyyyy4m4BmzO6VkCNj4OEkiX7bxPM9Llq2myhMCbdq0yRM7yosioAhkjAD7UMLMnyroM26ccotH0OsYXS56+pwi0BoBDrphZ/Y222wjG220UeubNfArTh6o6aYGGlFZVAQUgcohcMUVVwh+6v369RNCMyD0641U0Ndbi2p9FAFFIDECCPXbbrtNtt12W2P2QDO+8cYbEz9fKwlV0NdKSymfioAi4BwBFjLbtm1r/sgcD6B//OMfzsvJOkMV9Fm3gJavCCgCmSHQqVMnWbVqlfmDCfZzfPWrX82Mn0oVrIuxlUK2wvnGLb5UuPiGzP6jjz6SX//61/Lxxx/L8ccfL7gEKtU+AtjoMd/897//NQuxM2fOrLld2nHyQAV9jfbTuIat0Wrllu3//Oc/QlwWaMMNNxTO9iSa4J577plbnpWx5AjMnz/fJK5Xr5svJIdCUyoCjYvAn//8Z1m5cqV06NChAMK4ceNU0BfQqO0v9b4zW230td0/lfsqIbBs2TJZb731CqWxgKdx1Atw6JecI6Aafc4bSNnLBwJ77LGHfP755+bvC1/4gixZskQOPfTQfDBXI1xg/mpubjbcdu3atSY3JtUI1OuwqTb6dSCpjQtZ2+hffvllE1p27ty5Rui1b9/e2LCJmZ3lIiW21lmzZpm4Ke+8847AV/fu3eWb3/ympBUuf/rTn+TSSy+VZ5991vhan3POOYk7C/7axCbiFC34grDvb7/99rLbbrtlJvTg669//avhywph+OnWrZvB7Stf+UriOkYlRMgfc8wx5pxYZkJf+tKX5C9/+YuE5c/CN+341ltvyUsvvWSypv3giz6WVUhr+Hr99dfl73//uzm2E8bgC5MeJ2ZlxVecPFBBH9U7c3wvrmErwTov669+9Su5/fbbzQvKJpONN97YfOcF4IQo4m289957ctlll8n3v//9qggw+Pqf//kfGTVqlGywwQbmxbN8YXLhj1OMOGoRD4vTTjstVMC4xo2zAn7+85+bwZCFPgYehMKKFSsEzAjoRpoLL7xQzjzzzKoJCgarsWPHyuzZs80gGOSLNnzzzTdl//33l6FDh6aOLvroo4/KqaeeajYmgfHixYtlyJAhcvHFF7eCnIF6zJgx8vTTTwuuj7g6Mhisv/765hlmUgxMPXr0EAbaffbZp9XzlfrBgHjzzTfL1VdfbQ7thq927dqZP+oCXwxK4Pizn/1MevXqVSlWiuYbJw9U0BeFLf8X4xrWdQ1efPFFOfHEE4XwqHvttZfZWBJWBhEIESAIsXvuuaeiGj4vIK6OHIaOJspBFmFELBM7E7nhhhvku9/9bljS1Nfh6/zzzzfb6dHcO3bsGJonGi7a9J133il33323HHfccaFp095gULzgggvM7AINNCpqqOXrmWeeMUL67LPPLnvgRkFgYLEaPGYwwg7g1gjB10033SS33nqr7LvvvmawjjrgntDWzJCow7XXXls2X0nwpA8jvCkL7T2KLxSd559/3gzY119/fdUG7jh5oII+SUvnME1cw7pkGY1z8ODBcvjhh0cKrGCZdPrf//73MmHChIpoOPDVu3dvoxmW4jVBHP8HHnhATj/9dBk2bFiQ7dS/EfIHHnigMc3stNNOifNjgOQwiSOPPLJifA0aNMjMwhCyUQLLzzQCnxON0GLvuOOOsoQqZq+TTjpJttxyS7MLFfPViBEjTBsg5FEimEUQb6YUvlBAmElOnDixIkL1mmuuMW60ffr0KekENw5SQeA/+eSTFeHL3z58j5MHKuiDiNXI77iGdVUNK+SPPfbYkjq6LR/hde+99zoX9ghTTCFnnHFGpFZq+Qh+ot1PmTLFmA6OPvro4O2yf2OOQfPr27dvWXwhVDFzuBb2VpiSP/yVQ2jQ7CGgPcsh2oqBH7MaA/N9991nBg36Fhp+Gr4YHModhMLqYoX89773vcSDjz8vZh3Tp083Mw87k/Hfd/k9Th6ooHeJdhXzimtYF6wgtPbee28jdKJMInFloUE/8sgjggnARYdHaB1yyCGyww47pLIdMwjdf//98thjj6XKx19/hBbho7Ehl0sIY9ZBmHWgebsgFpFZ3EQzLZfsIHTWWWeVbV5igGaQtTMwzCLsRyhXmNq6MBPq2bOnjBw50l5K9clMAQXgxz/+cVlC3haOCZN3tdzB0eYT9xknD9SPPg7BBr5/yy23mEPH0wh54ON5bJvk54JYeIWssCg3T07oQYtk8c8FMfvhDN80Qh4+0E7R6FkEdUEscKI977fffqmygy8Gih/96EdmIbmczPBKse2GIkFe5JnUXBNWJnWjjnaHa1i6pNfBnjZIyxd9gT5B38iSVNBniX5GZfMyYLaIeil4CfGIwC3RBeFySX7km5bwrnEVegAbOnZUNM20hFcGC4kuiMVbPHPwjklLv/3tb82AllZowQeDIwLwiSeeSMuWyYO8yDMtUTcG7QcffDBtVkYog33UAnophdAn6BtZkgr6LNHPoGyCcuGS9tOf/tQskE6aNKkoF/g4H3zwwak1Gps54V/Jj3zTEF4zm2yySaR3Tan5M2hgO05DDGBz5swpyy4fVu6uu+4qDz/8cNjtxNdxCcRV0RXhqfOb3/wmdXbkEeX1U2oB1DHorllqHqTHlAf2rog60jdcKDnl8qSCvlzkavA5bNt28RJfbjSWgQMHFq0JsV2SCoeknitM28k3DeFDjf9+EkrKFy6j2K/TEJtoOnfunCiLpHzh5cLCbBpi1oZZg4E2jpLyRb/Bi4b+VC7xLHkk1ZqT8EYdqWvUTDUJv2AO9kkoCV/kQ9+gj2RFKuizQj6DctnQwc5CtvBDbEIJI9zf2BDikliIfffdd1NlicvaZpttliqP4MOYDjBvpCF2SiYVDknLQXClFQ7vv/++2YWatMyk6Vg8pT+VSzxLHq6JHbfUOQ2BeZKBsZQy6Bv0kaxIY91khXwG5bIIhucEfse4uPGJ50q55Ndm7Hdc0qKImN9pKW4AsrxQjv97GG8ubNfgGkd+Xvzfw/giP2LsoKHaBcy4MoL3GVjjBiA/L/7vUXzRd9JSXB5+XijL/o7ii7qmUSbAmj0QUWT5sGns7yi+SJukj9g8XX+qoHeNaM7zw22PzU+E3KXj/eEPfyibY9ux6ej2e9mZOXzQ8lIPfHHUHfsF0hDb86OoHLw22mijqCwT3YsbYC1fZJa0LePqGscYHmIszrNxK4zK4Sssr2pdV0FfLaRzUs4BBxxgzsSM0xKJGYPngUsiv7RTYtw08U1O6/Lprxd+/mljk2y66aYm3ok/37TfrQaYRqjiVUSsH9dEcLY0bcmzbChyTdS1lN3IwfJd7PMI5slvBiD6SFakNvqskM+43DhTAF4HixYtMptbbFwRvBHYZFQukR9BstIQfslslXdJeEOwMSwNIVxcCy5szf3790/DlhkQ0VBdEhue0MbTRGrkWfIgL5dEXdMqAWBO+A6XRN9IMwCl5UUFfVoE6+x5/MmJa4Lww1d6/Pjx8tprr5mofLghFvN59k9lo+Bgt2FaQU/IYfiy2m5UeUn5on5pFwYZODlYOslAmJQvhMNRRx0VVcXYe2ioAwYMSDQIJeWLqJYEkktL5EFeSSgJb+BFXdNq5QcddFAivOA7CV/0CfpGnHKVBIdy06igLxe5OnkOEw6C/corrzQLf2gzuBqyCMgZqYcddpg5YANtJI2mxEuINp5GCwRyXmJC+trY6WmbAbMNLyKRL9PSJZdcYsxKafPheTRdzqRl70FaIvwxftwuiAGWEMI/+MEPUmdHHuSVZNBOUhh1pK5pCb7A3tVsA1MjfSNLUkGfJfpVLhvfZQQ7u2JZ3CI+Bp9cw0aNpszi30UXXWQWowgby2Jt2heR58mbHa0uiJeZkL5JtOeo8uALv35CIKSxg9syiL9PaGYGj7SEjzkhe9Nqp/BB2xKMjHZOS+xjILyzC+2UPNCeyTMtUTfqmHatBT7AHOxpg7REX6BP0DeyJBX0idH/XOZPOFradLxIZixZlfipLBMi2NlJilAkOBMLYAg1FqyIeW61RoJUsVs2KFQIW0Ao3zS7MxGm9tAJF8IBPJkVELedQFZpBiFMSYR4cBWXnsGCncdsw08zCBHiljNpTzjhBGfdhz7ATtQ0fDEroz+5ChxG5ZhJkid5l0vUibpRR1cE9rQBbVEuwRd9gT7hQpEolw+e0+iVadDL8Nli0eqwq7PZgyksi1IIaIIzcVAIphfc9ErtcAwW5cQKBxqEMDyw89R1CFnyxz7KFButsFQPEELushhYCb44TOOqq64yAbuKrWlEdZtKxjG3IacxTZRqhkMQE3KXfpXW/BasP+tC+K6XE9oZjRlhWokzDyxfrE2VupCKkCdiJSEZcGeuNBWTB/4yVdD70aih7zQsuwuJjIdNHYEHESSKcK3E13ClQSPs0bzQzPEvTiIk8FqYOXOmELY3zclEcU3CyUXXXXedsWUniZuCYMBcw+CDcCh14Ivjx97H5MXh4YSYSCIkmF0Rxpmj6DiJybUwtXwh7DnSj9kas5k4X3b4Ij4R5gfWcirFF0KVvpXkBDPqghKByYfZAGYWFyYbi5H/E744svDDDz8UXJOTKBQM1swu8FJzNVv081Tsuwr6YqiUdQ3TzUDpeklnmT5vlPRpj9Vricyf8aCMH3mJXDNzkYj0k2Hjh8vJR/eWLu24/4HMGH6w9H35JJk+sr1MHT58dbqmgTLmjovltO90kVKCDGCHpBPx4mGCOeKII4wmhECvxoHJCAmOVMMf/hvf+IY5LcivsaLFsCsRLxbCK3BWaqVeQH8T8rKfe+65xizBIIcJyj8YwdfHH39sbNQMjr/4xS9MrHF/HpX4jpAAA7RgtEKEmJ8vhKg9m5U1DMxRpZyzS72ZmRD7B2046aDFzI/49AhuBiEGyC222KIg9BGiuHaixaNAjB49uqKDtcUehYIjHtGCUVii+OI9YGDAjBQ0Odr8XH3CF6GxCanM4rg9y9Yv9K0tnhAdzE54Tyo1KBarV5yg55AEpUQI/MdrHj/Ak6YR3vRPV3qe96n3+vjBXlPTQO/651s8rqxseca7fuBOnvS+3pu1lCvve9OH9fBEmrzewyZ7zebacq9l+uVebznUGzPr49CS//3vf3tz5szx7rjjDm/o0KGeiHhDhgwxv5955hnzO/ThCt+gfHjq1auX4QPe+OP3hRde6HE/CwKvK664Yh2+dtxxR8PvzJkzPXCtNjU3N3s333yz179//1Z4wRdt+thjj5XM13333edtvvnmXpcuXbzOnTt7J510UsnVeuutt7xbb73VPGvb0H7C10MPPeR9+OGHJeeb9gHKpGx4sPzYT+oJz/BebaLv0FbwRdtZnvikbWlj2joLgocoUtNNseGx6LWARi8zZXi3c+SDcY/K7f2/JoVV7SUzZHi34+XlUTPk8cGby0w0+kn9fLMAJgL+NN0KzxJ7nMBHmBZYXMK+jsbFFJsdoX6NLXYEL1oHvVgvCDCLI4AXniYQpjL6TzW1yHrBsh7qEScPCvKpHipbvTqskiWznpRJi7rLPjttWRDUpvx2HaXrziJzm1skdON5kTRMp1m4JGAXAp7j6FhsxMaLPdUv5KtXTy0prwi88cYbraKPYirDFKSkCBRDQGPdFEMl9toKWbxwgWCVD6NFLy+UxauSn86EnTHJLruw8vR6YyFw0kknGT9vzhUgCiRRQdMGP2ssBBurtqrRl9Xe60uH7TpLU8SzTbtsJx0U3QiEom+xqMURbExJL7/88lSHXESXVJt3r732WuMFwsI8i+Ocl6qzvtVtyeLpBRdcYPoOfYhF67wSC/a2n+OGCe+VIBVFZaHaVtr3PFBOaHpdnn31XWm1fWpZizTPFdm5a8eSPGrKYqNOH8KMdcwxx5h4O4RiwA0Szw+ltQgwAwQXTHx4Y+HVo7QaAfrK5MmTTRgP+hL7BiolQNNizsHo8Eg/ZyeuixAOxXhSQV8MlSTX2veUk0btIY+fdZmMfWHRamG/7FWZcPY5ck3XoXLl0V1a2+6T5KlpDAK4qqGl4rrJ7sQtt9xS7rnnHkVHEUiEAC6tuLHSd+hDCPk0p2ElKrSMRAzQ7Juw/ZxDU9KedBbGhgr6MGRir7eXboNvkJl39ZLFw3vIem3aSJuNfyrNvcZK8yPnSA/jRx+biSYIQcC/kQf7c9wpSSHZ6OUGRICd4P6TzOJOJMsKIvzwP/vss0Lxq1a1sg0Urrv4ou6VLlDMII84d6oMWHJaJJvBCOWAxsMmLDSdtKGEnTKomeUWgUmTJsnw4cNlk002MXGdOFshTbymSlYUuzwb6hiM8JqCb+JLlUpx8kAFfamI5iR9XMPmhM2y2WC6PXHiRLOvgFACbD9XUgSSIoC9mxAE22+/vQwaNCi3C9X088cff9xEdz388MPLVmbi5IEK+qQ9J2fp4ho2Z+wqO4qAIlBBBOLkgdroKwi+Zq0IKAKKQB4Q0A1TeWiFGuOB6SYnPBE9EH93S7j4FQvXYO9X4xOf6SBfhI/gdCtOkcrK1xwPC6KMzp07t3CIOHx169bNRButdGCuMOzx4yYwGod9v/POOybZVlttVYhumVVIBfiy0Sn9fHXu3Fm+/e1vZxbqAVdI2nHevHmFU85YR+I0NgLquYoYG9Ze5V5X0025yGX8XNxUrRLs0cmJwcOCEYdp77DDDiZyINvvcYfkPlvz+eSgkzPOOKMqgpWBh+iCnGDFAhzRHDfbbDOzwGX5IkokESKvuOIKOe200yoe8dDi/8ADDwihlImgiWC3fHF/8eLFJnolfBE6+Pzzz6+aoCASKW6IS5YsMTtqcUe0gw3th4srghY/b0JyVEuAMSDaIxlRGhCi7P6FLF+4SnKdCJHViI5K2fBFxFj6PxEs8QKzfHGQD2GMUX5wlaTfH3300Ybnav2Lkwcq6KvVEo7LiWtYx8UJggFvAIQVsXf8IVqDZeE9gGZNx+d0nUq+jLyAhPYlzC47DHnRwgi+OJjl/vvvr3iscDRS4pgjSJlJ+MMTB/kjLDBYoVmfd955RlAE07j6zaBIGc8995zBKy6GP6GKia3PQd4cMVmpGRF8cebBXXfdZWK4J+GL+P0oHIQ2rhRf4M5ATRnMJOj/ftffYLswQL700ktmIKrkuQLBcuPkgQr6IGI18juuYV1Wgxedw0NKPZmITl+p03+oH4PPkCFDTFzyOMHgxwPt+pFHHjHxxTkz1zUh5IlJXurJRAxEU6dONSYAdne6Fl7wRQx3hNXuu+8eKbD8mDAQEVF14403rsiJXAh5TjEjZs9+++1XEl8cB8lgD26uzUzwxewVU02pp5hV8qQwf9vY73HyQBdjLVL6WRQBhClCnpOiorTSYg+TnufwFSYfl8TLTb4//OEPzQEVpeSN1s9zHKqRZMctMwBMF/zhox1FVshzEEiSk6X8eTFLYq8AgoWD2V0SQotIqAh5NNMorTRYLmkx4SDwEciuiTzJmzJK5Yu60C7UjTq6JNqAtqBNomawxcqk7ekDDPj0iaxJBX3WLZDj8rGJnnLKKUaTjzKJRFWB55gJkA/5uSBeaMw12ErL5csKL+y8DBphhAmKw9OJ/c4f9mN8tMMIezaafCkzDH9e8IVg4bxRl4Mjp2ptsMEGRsj7yyvlO0IVoZVkcEyaL3mRJ3mXSzxL3aijKwJ72oC2KGXw8ZdPH6Av0CeyJhX0WbdAjsu/5ZZbhF2FpWrywSrxPEcdkp8LYuEVm3y5wtTywCDRu3dvs8hmrwU/sZuzSMkBH/wh7NmIU4wQDpzhW6omH8wLwYKJhUU9F1oqAxmLwphF0hJaN0fquRi0yYO8MIukJepGHaMG7aRlgDnY0wblCnlbFn2BPuFy0LZ5l/Kpgr4UtBooLS8hZ3fi+eCCWMAlPxcCAs2NhVcXxLSf6XmYgMCjaOXKlYWi+L7pppsWfvu/4MXiii8Gx44dO8oLL7zgL6Ks73iKwFdaoUXhDI6c58raS1oiD/Iq1SxSrFzqRh1dBAUDc7BPq+BYPuGLvpElqaDPEv0cl02cc15CF8KBavIyY2oh3zSEKQUNu1yTTbGysVsTb6QYwTPHOzJA8ceAMGDAgHWSYn745z//mXqW4c+YQShs9uBPF/cdt0AOtHZFzKSIf5+WyIM6uiLqePXVV6fODsxd8gVeuIRmaatXQZ+6W9RnBnhZoNUkoaSeK3hF5vXk1AAAIABJREFUkG8awrcb//0klJSvr33ta0arL5YnPPOSsqh82GGHGTfIYkIAIV/serE8k/KFrzZCOg0xMGHWSKI1J+WLfsE6RRqzEs+SR1KtOQlv1JG6hs3OkuII5kmjpSbhi3LZ6EUfyYpU0GeFfM7LZTei6/CuaOJ2l2O51Wcnrt3YU24eweeYHURN+RH2nHLFqU5hwhytP6lwCJYf9juJcA571l5///33zbqC/e3qk0XKNDHeeZY8XBNrKNQ5LbnA3s8DfYM+khVpCISskK+Dcv3ajP1ejXNvsZtHkeWFNP7vYby5ME/hHhhHfl7838P4Ij/c89BQwwaYuDIJ8Rw3APl58X+P4guf97QUl4efF8qyv6P4oq7UuVwCazCPIsuHTWN/R/FF2iR9xObp+lMFvWtEGyg/27Hp6PZ7HqpveakHvlg7SHvoN7tzo6gcvFxs5oobYC1f8J60LalrmpkoWIM5HjdhVA5fYXlV67qabqqFdI2Vg18ycWJcEvmlnRKzcEqMGJfEDl4OOklDeOLECdRS87caYBqhinsfsVhcE0HQ0rQlzxJewTVR1zRutxZri70r/ugbaQfsNLyooE+DXh0/y0EfixYtclpDXuz9998/VZ5EoSRAmUvCm4bDmdMQAtW14MLW3L9//zRsmcXOMI+icjMmVAPaeJqQAzxLHuTlihDOLmZAYO7Czu+vF30jzQDkz6uc7yroy0GtAZ5BIBNoKwn5p7JR6fGYSSvou3fvbqJQJtG4kvL12muvpQ68hg19+fLlJupjFAbcS8oXwoGt/WmIhWvcQZMMQkn5evPNN02QszR88SyB0sgrCSXhjYV+6mq18iT5Fktz1FFHJcKLZ5PwxYyRvlHuOksxHku9poK+VMQaJD0aFyF1kwiIJJCwyMWuyjRaIOUguAg1nHQQiuONl5AgZ/vss09c0tj7hEdgMHNBaLrE4nGxm/XMM88UIj26IAbYp59+2oS1SJsfoTHIK8mgnaQs6khd0xJ7J8De1WwDTzH6Rpakgj5L9HNeNuFZiZWe9kXkhZkxY4azmB/Ek7/zzjuNgE4DIfWifml91S0PxN/BV7qlpcVeKvsTH/Nbb73ViSspYaIZtNP6l1MZBrLvfve7TrRTNFzycjE4Ujd81cNCYrNZiR3C/MVtXEKZAPuomEZJG5a+gKmRvpElaZjiLNFPUXZcWNIUWbd6lKkp2k25wZ0Qpo8++qiZphM/xBUR1wTNniiUcd4bYWUSx4bNPzfffHNYkpKvEzb3mGOOMRusyt29C1/U6Y477khthrAVQLixGIj3StJNSvZZ+8nsDuGH5uxqLwPrI4QIYE2oXBs2szL6Kb75xWaMtu4cFA4RxmL27NmRdWBDl42qWW7ANWaKBEZjBzBhoStJcfJANfpKol8HeSMY2DmKsC5Vs7dCniPWXAp5YOUEHwJiwVepU2z4ssKUTVAuiRd6woQJ5gXnRS+V4Auz1PXXX+9MyMMDAnDmzJkmRk05Mw405unTp8u0adMiBWSp9WXAIE/yLmfGweBDzBzqVkzIww8DJkKeQHj8rbfeejJlypRIVrHz0wYcVEOblEpWyNMXKi3kk/Cmgj4JSg2ehs5K3Jvbb789sc2eF5D0PPfLX/6yIggyCA0aNMiYcZIKCbQ/4sujybvUmP0VxHwAZsw4OIAiyQAJXwg8NHk05jCh5S+n1O/whXbJIR1otEn4smY3jojEo6USfJEneSNQMfElGbjhnToww5g8eXKoyQaMPv74YxN51OKFoE/iOgxfViGgbWijOIIv2py2pw+EmZLi8nF9X003rhGtUn5xU7VKsIFZgtjaaCto6WhjfjMALwJTcaJBYra48cYbzbGDleDFnydCnhkD53biZ88MhPKtScfyhXcNvGOTxzZcacJkwDm2f/zjH41W19TUZDRKyxe8IITgH7PDZZddJscdd1yl2TJtRMhowj7gForJhLN2rV88gha7Mh4xrGFgrz7hhBOczjCKVRJzCQe7cH4uC6IEKWOnq5+vTz75xCgbCNOTTjop0fm/DAbM/jj0HKJuxMEvZQGe9ERN5ZzYb3zjGyaCqTXNIdxxx8QdmXfkO9/5jll8rcSgWAw3rsXJAxX0Ycjl/Hpcw1aSfSJIcrwg4VwffvjhQlFsOsKeya5CwhJXmxCYaIaYAfxTc7QqzhZlnaGUl9sV/wh88CJypz+mDnzhv3/ooYeaz7RugaXyy6CMIEcQorkSNx3i7AC8fQ4//HDZa6+9nJpqkvAIX2DFuQNBvuhf2PMZCEpZJ+DsYms+xMmA849LJQYi+jzRLfn0x5hn0AErFIhqCnhbhzh5oILeIlVjn3ENW2PVUXYVAUUgBQJx8kBt9CnA1UcVAUVAEagFBFTQ10IrKY+KgCKgCKRAQAV9CvBq9VF26rG4xh/flWoPAezF2J3Zrn/BBRfEbgKqvRoqxy4RUBu9SzSrmFecTS6MFRYsWQRkp2Tbtm2NtwCLSlnG4QjjVa+HIzB27Fi54YYbjPcHcd3xD3/uuefCH9A7dY1AnDxQjb6um3/dyuGVwik8G2+8sfkkvC6uY0q1hcC5555rhPuGG25oPvFUYRBXUgSKIaCCvhgqek0RUAQUgTpCQAV9HTVmkqpwTNpnn30mTPf5ZMNONTbpJOFN0yRHgI1YbNL5/PPPzSc+5Wp+S45f3lMyO2MdxhWpjd4VklXOJ84mF8UOC7Djxo0zW+DPO+882XPPPaOS670cIoAQIMYLAee+/vWvC6acLDbq5BCammaJzXWE827fvr0J8UBICDaIxVGcPFBBH4dgTu/HNWxO2Va2FAFFIAIBPOGI4UN4BeLxvPTSSya0R9wu4Dh5oKabCND1liKgCCgC1UTgrrvuMkKeMtdff30TfC9JMLU4Hr8Ql0DvKwJBBDAboGmgefhPeiKgGGe67rbbbiUHwMImedttt5kDtk8++eSyzEmWr1deeUUIYGaJYFYEYbOB2Oz1an4SH4gDNvz7FuCLmEBZxJOxdQd3gtA9++yz9pIxG+y8887m2MeszEGYMDh9au7cuYVD1zFnwBftmNV6hI3DQ3tydKElzJ/f/OY3U8d4IhYTgdvwilu1apX5s0HdbFnlfKrpphzUcvBM3FStEizSyYl6ePHFF5ugUkQWJJqfpcWLF5vF3UceecSEaeUkqLgpJ8+SL379nAeLbz9RKB9//PHELw0CnkBVhEWmvB122MF8ohFB8EXEQgJ4XXjhhea4uWoIMPgiMBcLp0T5JDQyESwtX9QbbY0BALsskUGrJcDYO/Gzn/3MRPNkgAb/du3aGbyWLVtmTsmCL+z/xOyvVpA6Bhz4+sc//mEEJ5j5+aJvoFxg2vj5z39etTDADIhEPcVmjkCnPW3fxsRC5Eri/NOeHBvIiVLlBKlDEWATHBFOEfSnnHKKed9Mw0T8i5MHKugjwMvzrbiGdc07goFOR2RDXvooLYMwt2g8HNpAiNu4mNwc73b11Vcbf3D4xiOI6IRJDgWhHLyGCE2MZhzFF+FkERIcQ0hMeg4vqRShkXL4NS8sMxx/OOdgmZYv4tD/9Kc/LURZDKZz8ZvBhXNVOfKQCJVRfFEe5woQQZL2IIxyOcIrCd8MiuzwpSwiVMadNoVA/fOf/2zanRPCrNBNUlapaVAirrvuOnMSFoOiDTNdLB/4YrbLKVb0s3IUCtqIWRaKVNIBNk4eqKAv1lo1cC2uYV1WgWPaENgc5hwnGPzl0unxDLnqqqsihWq5gp7BZ/DgwSacLppfUiIOPJoZh6JweIlrQsjjxoogLUVDR+BzYhaDFodWuBaqli+EBya2pARfCFXMCZU4rAUhz7F9DPBgFiVIgzwzMDB4czBIOUI1mJ//t+UL3Eo9SpMZAJixQdE1X34e7fc4eaCLsRYp/SyKAHHUEfLHHntsSUKezBgUeG7EiBGtYncHC9p///2NTz9+/fy9++67JkZ7MJ3/N5o8Qp78SxHy5MG0nxcX10TWBVySFaZ9+/YtScjDAwIOvjjw48orr3TJlvHJPuigg4wgLUXIW74wLSHwEcgIQFdkhSl5U0YpQh4e0P6xa1O3KL6IC8Sgyx+HmyQh2oCZT6lCnrwphz7AgE+fyJpUo8+6BcosP24ELzPbVo9Z2zk2eXuaTqsECX+g2SNUicUSNsXGNknsFgj7Jod+hxEvNMIqzYHS5I2Jiek16wGlaN5hfHEd+yo2ZU5uKpcQepiWmAm5OgkLcw02ZARjGkJzHjBggDHjpcnHPstA+7vf/c4cVmOvlfOJZt+tWzeDWfB5/wlT2L3pj3EnTKHgoKCkOXwePjgJizUPjjusJMXJA9XoK4l+jed96aWXysCBA1MJeSBAs991113NQm4YJHgtcJ4pf1FCnudZ4MS8EWfHDSvLXseejxZpTx6y18v9xJTEolwaIU/ZaLXYxFmcjdJSk/KJGQHB5eKQ6n333dcc9YcSkJbIg2MDyTMtUTf6DnUNEidCoWB84QtfMAvhxAfCMyuMwBzsaYNSZxjBPOkL9An6Rpakgj5L9HNcNi8h2huLTy4ITwVmBmkFBC8hZ3ey8OqC0OTx5CgmIErNHy8QV7uMGRwxSXFkXVpiDQTzWFqhBR8MjqxtsPaSlsiDvKIW0JOWQd2oI3UNEoH7CBVhiYVS6/lkr/k/wRzsS1mP8j8f/I6SQ9/IklTQZ4l+jsvmzE60ERfCgWqSDxoS+aYhFt7QzlwIB8sHgxmLZmkIOyz23FLXC6LKZBDyn8kblTbsHgMjboGuBmzK4XBstOe0hPmEvFwRh4lT1yCxrvD3v//dxAQiPhCCvn///sFkhd9sWnJlyiNTZp70jSxt9SroC82rX/wIzJw5M7HQSuq5wouIJ0IawrcbP/kklJQvzEC4s6UhDtZOKhyS8oV7nV23KJe3t956K7EnS1K+WK/B7p1mdsazmDOSrv0k4Y3BH6+d4OwMrxdwOPvss4VDvOmDYWtF4MysAOyTUBK+yIe+gbDPilTQZ4V8zstlk5HdqOKKVfLz7yYsJ18WbaNe0nLyRNj89re/LefRwjPglVQ4FB6K+eJi1oIGy/kDrglPFBY1yyWeZYbnmqgrdQ4Swv6cc84x5sMk7o4usPfzQN9gVpEVaQiErJCvg3L92oz9js99pSnKvkrZlpfg9zDeXJin8JSJo1L5Ir899tjDaKhJZwtBHnBVjRuAyuELn/e0FLfQ7OeLsuzvsHYkDXWlzuUSswFcIqPI8mHT2N9RfJE2SR+xebr+VEHvGtEGys92bDq6/Z6H6lte6oEvFga32WabsmFlFrVkyZLI58vBy8VmrrgB1vIF80nbkrqmmYmCNes1/fr1C8WsHL5CM6vSDTXdVAnoWiuGqSsxPFwS/sRpp8QsKmImcUmYEY444ohUWSIg4gRqqQVYDTCNUGUhENxd04IFC1J5peDRQngF10Rd07jdWqwt9q74o2+kGbDT8qGCPi2Cdfo8rmr4/7okNuyQbxpioxQBylwSC4OYSNIQwsW14MLWzOakNGQ1VJeCixASaONp1kp4ljzIyxVRR7TxtAIVzIvZ+dPwyWIwcaKyIhX0WSGf83IRyC+++GIiLv1T2bAHeAnxmEkr6AkQRhRKdrXGURK+yIOQxnGB1+LKwoa+fPnyRAuUSfli4PjRj34UV3TkfTRUBFeSRfCkfKHNDxo0KLLcJDfJAwGYhJLwRh2pq9XKk+RbLA2YJx20k/DFjJH+mmQRuBg/Lq6poHeBYh3mQadk12jQVa3cquL/Tn5pOzsv8RVXXGEiY5bLi/85XkIWd4mXkpYIT4tXkAtCMBA2AnfBtET4AyJjuiAGbM4hYKNTWiIPQhe4mm1QRzxr0hKYg30SZSJJWfQJ+kaWpII+S/RzXjbbwInymLbD8zwvIfm5IOLcEwsm7bQfAcPuX1e7FonRw5QfE1VaAq+77747lXnE8sBshbUN4q6kJXzQiWJarheQv3zyIK+kM0f/s8Hv1I06uhiwMSuBvYvBkb5An6BvZEkq6LNEP+dl8yISH33q1Klla10IU54nHxfCAch4EYlfwgEnabRBhBa+3GnNNrYZmW0gIH7/+9+nGoTQctm271I4XH/99Wa2kdQkYevk/+RZNv0Ql94VkRezvbR8oTVTR1cE9rQBbVEuoYjQF+gTac1J5fJgn1NBb5HQz6IIEPCLKTZx0ksVqqTnOZ53FTjMMklUR2yp5Wj28MVMhfjqLoUWvBHrnVjy9957byJ7va2P/USwsLGGk7xcCgdMZoSb5hCNcoQqJrzp06ebGZBLvsiLWRV5l2MmpC7UibqlNQvaNuATvmgD2qIcYY9JkD5AX0h6eIi/fNffNUyxa0SrlF9cWFLXbLDoxMuEBpzEfY0XkEVTohPaDSWueSK/Bx54wOx2JPxukqiRTKUJ70A9KnliEtv7OZGL4GuYFOJ8xhEMzDAqdeiIxR5hysBLOXEncvEMZjfCHXDEY7knJtmyoz6JA0OkVMIIE346zg0XvoibxAwDe7qr2WKQRzZ1ESsH/rDdxwU6Q4lghgJvhGB2NVsM8hX8HScPVNAHEauR33ENW4lqcNgHx70R7RHhhbAgfABCjA7OVJUXj47OGaRoWpV6Af31Q3jZ8zwJV8u5rJtssokRFpYvXCiJZwO/1TprlDIJ9YzGyiDEAGn5gn+EO2nw+uFA6MsvvzzyJC5/ndN8R3gRQ4doogh9ArFhprBxZ+ALf3QOQOHsVgZETBkuNfli/MMXIaiJTspZtcRGYvOTFa70r48//tisgSDcWZQ/77zzKs4XvKJQgANmQwKx8Wn5YtCh/VBuWCtgs9XIkSOdrK8Uw6nYtTh5oIK+GGo1cC2uYStZBQQ+01kEpz9GDAGjevbsabaQV0PAB+uI1oVNdM6cOYY/Ao1BbIbCTx5zT9JpNEKHAWH06NFGQHOmbVyc/CA/9jfCnNkNmjG4+fniQHTixuA2WmlBavmxn/CF5glm8+bNK8RMRwsFr969exvtutp8gT1YMfNiZ7CN5Q5fHC5y+OGHm9kIwraaBF+cB4s5kvOQbWRR/OOZUTITYaZYDl+0BQNGueanOHmggr6aPcVhWXEN67CohsyK4+bQxrfcckv573//a7RIBE4WA1hDNkADVXrs2LFy7rnnmkGM/kUI6FIH1zh5oIuxDdShtKrJEcDc0r59e2Obxs+eqIhPP/108gw0pSKQAAFmoaNGjTIzYcx6bCpkFumaVNC7RlTzqwsEmH6jyVsi7k+HDh3sT/0UMYds77333nLMMcc42yhWLWARsJj04J+Dw7MiTFOsjXDMIYSwnzt3rnN2VNA7h1QzrAcE2E2KHZbNLmyt55zRvn371kPVnNQBG/rw4cPls88+M2sOLOqW4x7phJkSM8HWzvrDG2+8YY4YRIPOStiz4Ixt3hJhNOLCStu0pXxqmOJS0NK0DYMAtlK8hzDXbLDBBnLooYeWbDetZ7DwEWfWYw81QViBVS2sYdCuzNC22GIL00R4iOE6evrpp1e9yXAOwFOM3cH0MwhvKNekgt41oppf3SCA0KoFwZUF4KxfBMkKquD1vP1mFsK+AEv47mdJeO88++yzZnaE11o5Xjtx/KvXTRxCOb0ft8qODRItSwVVThvQAVuYIIj+iD93JYRDFIu42B5yyCFmvwR7FTDbsL+i2nxE8Rh2D9y+9a1vCe8QgxOx4vF7P+GEE8Ieyf31OHmggj73TVicwaiGZSPJuHHjjNcILx5xYWrhBSxeU71aDAEGcuzM9APMEOxcLtfPv1j+Sa4RX2b8+PGmn7ELuJaUCvzWscuzwQ+/fPYy1DJFyQPqVUTQL5H5U66WU4+6SmZKk/QbP0MeH9xN1k508gLH5zJ/wkDpev/B0vz4YOnijMElMv+PE2ViSz8ZdWIe670a/7CGRdPCmwAPEaanLCayUHbttdfmpeGUDwcIsGbArlU8NhD07GZlo5gO6A7ArcEswuSBrco64nHV/Afl7KMekU6TF8pKr0Wm5lLIW/Yr8Llklow/8WqZvbICeVc4S7Q8Qqt6nldwDSRwFwJBqb4Q+MMf/lAIWYCfP66gCHslRaAYAiGLsRvI5pt8KYdafLEqNMY1ppq8yGjo9pR7GyyMOC8Qmjx+uMTdIHYJAiDNturGQLY2a0ncdfoEGj2Lifhh29grtVkj5bqSCPgE/RpTyMm/M+VN67uFXNM0QqY/f4BM3fNEeeGEC+XQxbfL0DtflaZh02Xe6D7SftUimT3pRrlg0DUyk6d6D5Pxl54sR/fpIu0KXK+QRbPvlxsvGC7XzOQM0n4ybPxwOfno3tKl3ToTisJTIuU8l+yZVYtekEk3XiqDrpkmIjvJwDHXysWnfUe6rJopw7v1lWtg8+Tust4lI2T6vHNFrviu9H2hr9x26GL52dA7ZRG4zBslfdovk/kzHpTxIy8JqdsHMmP4wdL35ZNk+sj2MnX4GgyaBsqYOy6W077jx0kEswuBpCBikEDE+8D1ChcsbLIQUQeh4447zgTuIiaLf8s0Zhvc3zhEG43e1YEfplARI2DgD36ZLeD7y6IWgajwGqiU54AtP+zTxiIhVIHlCwFIGAMiD4JbFqYNy9crr7xidj4y+Fq+dt55Z3O8YqkxTq677jpTHwKSYbphC305daMNib/Djkz4gugzDCQc+1gqX2FtU+p1Zqe4a+KNsnTp0gJfe+65p3zzm99MHLOo1HLj0lu+2NSEwsVMikib8ES8G4L9+d/FuPyqdd8naTeULoMfkJXN46Wf9JBh098Xr+VK6fPl9URkkcyc9Ip8ZcSz4q18V2ae0lPar/qnTPlxPzlsxrYyumW5eN5KWfrrHeWp44+Sc6b8U1Y7LK2Qd6acLz0Oe1I6jJ4tKz1PvKXXSdenzpHe5zwk74R6NZXzXLJnVr0zRX7c40iZKKdK89KV4i29V3rNvWA1P+36yOh502VYE2sTr8tK6t9+DUQz/yDPfGWozPeWS8vMU2WP9stk3oTzpPfxTxXqtrLlMunw1DnS9bCxMnuZr3LTrpCRk78kJz/ytng8f1cneazf+XLL7E8K7Yx2ds899xR+I8SHDBligmFhimEHHQtu/PXv39+kwweXBbBgxyIA1x//+EcT9pYO6eplhccRI0YYT4ubbrrJCFOEC9Ei+US4EhURv+Qrr7zSDAiFClXwC3xRHi8c28nxk7Z84SvNTOj2228XhMSPf/zjqm3sQcDTprvuuqsZbFm8RAMHL/jC2+N3v/udCWV79NFHl8QXdcHLhY1L2OZL9b0mGiNRGAlEh0ClD8EXf8wECXR22GGHmeMfbVCxCjZhIWvK4shJyoYHePHzhckKnuGdOlSL8CqijQisRpvRdrQhvNGmtC1nLtDWtDltnydaZzF21fwJckjXX8ku05+Q0X02F1kyw2i5k05Yo8Ub7lfJkhmXSLe+C2RU850yuMuGa+q05vrxIneh8Qoa8vHy8qjAgq7Jc5jIXWvKCCJi7sc91671Yuwy+Ez4zCWd12jkCPFAXTr8byCfNVr5pH6+Z2QNLufIB+Meldv7f22tmasV75vLTDT6os8W4TWIQ8TvuMWXiEfLusULxgIgMcPj4qvjboeGyKEgzEgqGZOb2Q7xwuGJgS8qjjl8MQigwTLLwVOkUoTmd/zxx5vs991334I9Paw8f/z+s88+e53BO+y5Uq/D1/nnn584vjp8gRcDC4N4UKkotfyw9AhGQg4/99xzAl5xZx4weBO/HyWGk6VcKTNB/uALpQYPHaKfxvFFKGV7BOFdd91VMb6CfMbJA59GH3w06vdHMmvqNFnU1Fm267C+L2Fbabd1Z9l50TSZOusDWTLrSZm0qKPsst3mawUhqdt1lK47t8ikqX+VJb6nV39dVcZzCZ9ZtVCeuf8ZkZ07y9YFs1Fbad/nSmnxHvANWOswFbhgy+su++y0ZZG6icxtbpFlgacKP039Y9IUEmf/hVkEIQHQGomrHneIBvd79Ohh0g8aNMjMQipRC7Q/4qwcdNBBZtocJeQpH77gHwE8ceLEivK1zTbbGK2TwRGNL44QICeffLIwoDJwVUIjRMgfeOCBRlgTXz6JTR++BgwYYMwUleKLupI3phBcROOEKVjCu42RT52om2uyfNEmzAST8EVb0+Y77LCD0AcwPeWByhT0a1hfdJX0/fJ6xpeXEYW/9bqeLFi+19JsuabvFq3StFmvu5w8DUN4FJXzXDnPRPEQdm+FLF64QKJqsOjlhbLYZ70Jyynv1+nkN998s+noSQSWvz6k57g/tCHycUlo8oMHD5Zjjz3WHJxRSt4MCPhNc3gFh6O4JAQOp2oxjU8iGPxlMxAhJLBJc8CLS8K8xYEYxOtJchKXv2z4wv7MjMi1sLfClLwpg7JKIepCnaib68GRNqAtaJNS+cKkSh9g8K7EIFQKRqRNJ+j7jZfmlZ5x58OOvPZv1mqzj+FmgIxv/o/v3tp0LSzohnJcznPlPBPKQMSN9aXDdp2lKSJF0y7bSYd06EbkXp1bdFA6OTsGS+3olkMr7MkHYeOCrHBgo0upg48tn/owE2BR02UwLkxbLPyWKuQtX3zyPNN/l4MjsfUxb6XhC0H83nvvmaiVfn7TfOfgGvIk73KJOlE3l4Mj2NMGtEW5BF88T5/ImsoURV+Rngf1k6a5L8mri1b46rBKls2+QQ5oc7RMmL9C2vc8UE5oel2effXdNYuza5Iue0GuPaCzHDRhXuvr5nbbMp5L+Ezb7WTfH+4rMneBvO1bLGVd4qA2HUP48VWv8DWqvBZpniuyc9eOPs+jwoM19eWqq64ynbRcYWory/N0dusGaq+X+4kWzjGGeJykITR7TgRydXA5pqTPP/889Q5RBiH4QnC50FIZyBBceG6lJU5RYsbiYtAmD0yC5JmWqBt1dDFogznY0wblKji2Pmj29IlqLmjbsv2fZQr6ttK+96ky7pCn5KyLbpcXjLBfJcvmPyRAaMTBAAAYOElEQVQjL7hZZMwFcjQLtO33lZ+M6yWPn3WZjH1h0WqhvmyeTBl5qQyVM+XKo7sUn1KU81yiZzaUzof8WEZ0fUBGXj1dFmFaWfWOzJx4v0zrPXQ1P8Z+/sXVGP17mfjGAz9uIu17ykmj9gjU7VWZcPY5ck3XNXm1fqKmfvEScvgGmpILIh+8gdIKCF5CPGisi2la3tC68F7BzTAt4ebKoqULwga91VZbGW+rtPn95je/Mbb5tEILPhgc2Wn94IMPpmXLnKREXnFrK0kKom7Y6qlrWsKTCeyTrGEkKYs+Qd/IksoU9Bh9vib9x06Wu3r9S4Z33EDatFlPNu79sGxx9v1yz/l7rNFm15et+l8pM+/qJYuH95D1sONvPEAe3uJUmXXPmdKjsCAahKCc55I907bpOzLqnntk0MprpeN6baTNervLyJXHr+WnbSc5ZPgJsgI/+i8NlgcWhLlJtZdug28I1O2n0txrrDQ/ck5E3YJ1zedvPBqSLLwm5Z4XkZfa7g9I+lwwnXWddCEcbN4MQgxqaQgzF3FT0s4y/DygDeK5kYYYGJlJscfBFeHa6HcFLjdf6+JZ7vPB56gjdU07C+KAcrB3RfQJ+kaWtvp13CtdVU7zqSwCce5UaUs/7bTTZL311ktk02WHLp45cYSrHuFtMQmVS8QNnz59eqIFxaR84aq3YMECmTx5crlsmYEC90N8wOMoKV9sYLr88svN+lZcnmH3MWWwHwO/9DhKyhf5kDZNtEpmdmi6SV1ck/L2yCOPGK0+jaDm3SIwYJIZUFK+ZsyYYdxHWTSuBMXJg/I1+kpwq3nmBgGETLt2a/c3u2CM/DitKQ2xMaWcHaBRZbKGMGXKlKgksffYhez6ZCAXsxYGVzawuSa8lhggyyWe7dy5c7mPhz7HQSjUOS0lEfKllEHfoI9kRb4QCFmxoOXWKgJoM5bs9ySavX2m3E92S0aR5YU0/u9hvLl4qXEPjCM/L/7vYXyR3x577GEWGMvVUJctW2ZmUVG8+Xnxf4/iy4YliMo37l6cicXPC3nZ31F8IVCpc7nEDAgTYxRZPmwa+zuKL9Im6SM2T9efKuhdI9pA+dmOTUe336tRfWK7RJHlpdp8RfHEvXL4IvQFG2/KJWZRbNePonL4crFDNi4Pyxe8J21L6ppmJgrW7K+Icvcsh68o/KtxT0031UC5BsvAbBAnUEutFpoWAbPSEAunaT13guVjRiDyZxpCQMQJ1FLztxpgnECMyhevojQabljerGmk8UrhWfJwTdSVOpdLFmuLfbn5BJ+jb6QZsIP5lfpbBX2piDVIeiIXurB1+uFqaWkxURH910r9TmgF8nFJDByYSNLQjjvuaI71S5NH8FlCUrOQmoYQLk8++aRTswHxXDB3pVkr4VnyIC9XhHCmrmkFKpiDvUviyEf6SFakgj4r5HNeLoKewGRJyD+VDUvPS0h+5JuGdtttN/My25C6UXkl4YvnMY8QsCoNEVQLk0GSBcqkfM2bN8/Ec0nDFxoqgivJInhSvtDEiWGUlsgjqVafhDfqSF2tVl4uf8TQAfsklIQv+gR9o1KB15LwqYI+CUoNmIZOiaugi52GwIf/O/ml7ey8xLi+udjgBF/MDjikhciXaQlXQbyCXBCaLmGfXewaRaASgdIFMWDPnj3bnIWQNj9CcZOXKzMJdXQxAIE52LuabdAnkrqRpsU07HkV9GHI6HUTyhf/3yTacxRcPG9DA0elS3oPH/+//e1vibTnqDwRMIRRdrVrEU2QKb8Lkxe4X3bZZam1U+rPISLdunWTV199NQqORPfYSPeDH/wg9YBNYQz65EWeaYm6UUfqmpZQJsCeNkhL9AX6BH0jS1JBnyX6OS8bl76f/vSnMnXq1LK1LoQpzxP/vVwXwSBM2Hdvu+02c/BEGq2L3bD4g7uKl4+AYFflE088kUobZFBECKLxuiJ2jKJZphmEmN3961//MkLQFV8IVPJMM3OkTtTNVSwl6gb2tEGamRB9k75An0hrTkqLtwr6tAjW+fME/MKv+NFHHy1Zs0eT5zmedz11RTiffvrpcvfdd5csVBl8iNWCz/VFF13ktAUZzCZMmGCOckxir/cXDl8IFhYp77jjDv+t1N8RWvfdd58Jy1yOsEdjRvNm0HYptMiLPMm7nBkHdSHIHXWjji6JNqAtaBPaphSi7TnOk77gSsEppfxgWg2BEESkRn7HbXl2XQ1eJkL6YmdP0nHR0Jj6Dh8+3LmQ99eNiIWEQE5y8hXPIRh4hsNHEPIuhZafL6IVEuUR2z/niSIwogjBgPa39957V/QkJ+KtEJ552223NYHh4nbfwtdLL71kNl2NHTvWuTC1mMDXOeecY1xUWXCPc91EiSBuErMBBgrXQt7yxaYuTr7CkYCQw3F8MSCQljWkW2+91dls0fIT9hknD1TQhyGX8+txDVsJ9hHel1xyibzxxhsmqiXnZbLlnBACTFM/++wzWbRokTnMnAHBpbkmqj4ICc6KtTFw8KO2fCEQ+COoFAvC8MoU30XI3iieuIfb5i233GJO2mJWQ3ArvC8QFpYvtsWDJ/jBV1rvnzieuI/wYuC2oXg7depU4AtBBS/wzqCIWyDmFXuaU5L8y00DX5g5fvGLXxgXSdoRMx1txkDJoIOf/JtvvmkGxWuvvdaEmK7UYO2vB8oB/RleOD2qQ4cOJuomA6Xli4V9NlvhLMA6Uhr3U3/ZSb7HyQMV9ElQzGGauIatJMsIVg5u5lBqprUsjOIjzG5CBCjCqhwNC43x3HPPNazfeOONRsMrpR7wxUHXhJlFeKJVwxfBs3r27Gn4c+FdQ/6cboUg5KB2IkxGCRuEJtonmCHYH374YVMtDrkm3gt4ueCrFKxIi2ClLphNXn/99QJfHDTDwibmMbTrqLqVUqa/fZnpEba6GMEXswjaDzfHSZMmmWRsauvevbvRrPGMccVXMR7CrqGpI/RxC+XQFAi+EPwchEP47GoKeMtnnDxQQW+RqrHPuIatseoYgcOxg3azC+eHjhs3ziyW5qkuCG2ChCGYN9xwQyO4jzrqKEG7VApHgLNTWeBkXaRt27bmfNiRI0ea08vCn9I7SRGIkwe6GJsUSU1XUQTQKAmPgBDgDxMHGnDeiGk6JhiEPITgYu1CKRqBV155xWD2hS98wbQv4apduFVGl6p3LQIq6C0S+pkpAgh5f2wdjl/jgIs8EsLKEjy78N22+dXrJ6YNTDKWli9fbo6DtL/1s7IIqOmmsvhWLPe4qVrFCq5QxphEiDezcuXKQgnsmszC3llgIOQLpho8KzzPMwvQnLbkYgdrSHF1cRkh/61vfcu4KXKgDe2MRl/OWk5dAOK4EnHyQAW9Y8CrlV1cw1aLD5flIOwfe+wxkyUuk3kU8jCH0MLDh4VVYvckcTd1iVOt5lUr7VuL+MbJAxX0tdiqIhLXsDVaLWVbEVAEykAgTh6ojb4MUPURRUARUARqCQEV9LXUWsqrIqAIKAJlIKCCvgzQ9BFFQBFQBGoJARX0tdRayqsioAgoAiEIEFYjjNY6BIel0Ou5RYAFGCVFQBFQBECAWDuE1ChGKuiLoVID1/DhVlIEFAFFIAkCarpJgpKmUQQUAUWghhFQQV/DjaesKwKKgCKQBAEV9ElQ0jSKgCKgCNQwAiroa7jxlHVFQBFQBJIgoII+CUqaRhFQBBSBGkZABX0NN56yrggoAopAEgRU0CdBSdMoAoqAIlDDCKigr+HGU9YbEwHOLZ0yZco6lefMXK5zX0kR8COggt6Phn5XBGoAgTfffFM4/GT+/PmtuP3lL39prm+++eatrusPRUAFvfYBRaDGEOjUqZPh+P333y9wjhY/ZswYuemmm/TUpgIq+sUioILeIqGfikCNIPDFL37RcPruu+8WOL788stl9913l5NPPrlwTb8oAhYBjXVjkdBPRaBGELBHF86bN89wPG3aNHn44Ydl8uTJstFGG9VILZTNaiKgRwlWE20tSxFwhMCRRx4pW2yxhWCX79Wrl3Ts2FEeeughR7lrNvWGgGr09daiWp+GQACtHpv8IYccIi+++KLMmTOnIeqtlSwPAbXRl4ebPqUIZIrAXnvtZcq/+uqrZejQobLLLrtkyo8Wnm8EVKPPd/sod4pAUQS23HJLcx1tvphPfdGH9GLDIqAafcM2vVa8lhHYbbfdpLm5Wd56661cuFMOHz5cZsyYUcuQ1jXvuhhb182rlVMEqoMAx1pusskmwtrBVVddJX369KlOwVpKIgRU0CeCSRMpAopAFAL+84tV4Echlc09FfTZ4K6lKgJ1hYBf0NuKqcC3SGT/qYI++zZQDhSBmkegmKC3lbICH5//Pffc017WzyoioF43VQRbi6odBKIEV+3UIh+cfvLJJ7J48WL57LPP8sFQA3Khgr4BG12rHI+A53nxiTRFAYGwgXHbbbeVkSNHyoABAzQ8QwGt6n9RQV99zLVERaDuEVABn68mVkGfr/ZQbhSBmkZABXw+m08FfT7bRblSBGoKgSFDhsh+++2nJpqctpp63eS0YZQtRUARUARcIaAhEFwhqfkoAoqAIpBTBFTQ57RhlC1FQBFQBFwhoILeFZKajyKgCCgCOUVABX1OG6Y22PpAZgzvKW0OmiDzV4VzvGr+BDmoTU8ZPuODNYmWyPwpF8kBbdpImzYd5aAJf5Ml86fKtRfdE5lPeAl5urNKlsy4SDq2OVomzP88JWNBnObJujCvkmXzp8jwAzoKvuxxbZGSoVSPr+4HLnDxs0H966Xv+Ovl9rsKerd4am5FEGjbZbBM9WbJ6D6bm7ur5j8oZx/1iHSavFBWei0ydfBXZdb4i2Xo7LSCsUjhNXxpXZy6yTov7Kr58sDZZ8mkTuPk7ZWeeFMHS5d1EtUwCLGsfyQvaN+JRamhukQsGpqgighsIJtv8qV1BVcVOaiNohLitPkmsrG+zbXRpFlw6SkpAgkRWNkyy5s8ZqDXJOKJ7OQNHDPeGzNwJ0/6jfeaV3qe9+l0b1hTk9d72NjV10W8pmHTvY+ax3v9pIc3bPq/vObxA4gtsPav6UjvxON2XPvbpHu/OEdLm73p44d5vQvP9/OGjZ/uNS+l8JXep9NHeE0ywLtt+jTvevgy6fp5wyY+77WQpEDLvZZZd3rDejetTVPIp5DI81a2eLMm+srrPcwbP73ZW+pLYtJMHuMNbFpdp6aBY7z7DEYDvPHN//GnDHz/1GuePj6Eh/8UwWmEN/3TVpXwVhpcfVga7F7zpg/r4UnvYd5ttq2a1jybpD5eQmwCteHnypbnvYnD+q3BlH4w3pve/Gkh5Wp+W+MS94x5OMB308DrvWkm3/dX17XQH+hj767pB/28YbddtaZduE6fWuktbZ7ujQ/l0d+H/uSrC339iTX9zNQ0kI8YvNfpG4WaZ/9FsmdBOagJBJY+743pvb3Xe9jkNR3+U6958ojVQreVoBdPmgZ741//1PNWvus1L/h0jUCyL5u3zm/PW/PC2nyKAvKxN2vMoV7TwIne60awI1imeSN6b+/1G/+6t7Ig6Cl/oHf98y3m2tLmyd4w+B7z/BoBvdx7e/KZXlMhjed5S+d64wfu5DUNnuy9bWXpyoXe5ME7eU0Dx3nPtyxfLSRen+gNbNrJGzx5obc62WqepPcIb7IRPAgSymMAaS3QWlfpU+/18YNb8bCy5ZnVg1Pv671Ztn6FATJk4CPTla974/s1mQF1tUi1wm8nb+D4ud5SBHfzQm9povokxKZ1ZcyvlW9P9gY37eQNvP6ZNYOqreOZ3uS3wc+2+1pckjzjreF7LcbBfIN9xwprKfSVlS0LvAVL/89buqb9CjyubPGevx7F5VBvzKyPTRuvVhYQ3LZN1/azQh8y70KPNfhSs+Vey/TLvd6RbW4gyOyfCvrMoK+lgte8PFYzLLAeeMmMRr9ai1+rx9kXPKWgNwLNCvUCA74v9gX3C2JuB3hfM+tYPTj4HjfXLY82r7VCaXXKYnnZZ2xeYc/a+3bmE+TTXm9aM3Cti5svh7VfwwR9q7YK46lYfdaWXyikFTaFq74vgX5QuLP6OrM6+kNrjb6UZwIYt2rDYD62roFn1igTrQZzw6f/+ehn7cy1dT0Klc31F7XqZWEvq7kyP5JZU6fJop07y9bt/F2mnWzdtVN1atO2g3zrO91k2iW/lYdemCFTZsyXZUVL7i777LSlz/bfVtpt3Vl2XjRNps76QJbMelImLeoou2y3uS+NiLTrKF13bpFJU/8qS2RNfZs6y3Yd1veVUiyvTtJ163brpvFdaf111RoegnxaHkTmNreE1K11Tsl/lVKfOGyKlLrkrzJ10mxp2mU76eDvHrK6fyya9KTMWhLwF0r0zL9lwTNPyDQJYNy+j4xuYRG/yOJ0EfbMJVNei+y8z47SVIRHmbtA3l4W4LGQ15p+viZN2447yXd6PyOXjH9UXpjxqMyYv6SQMq9fWlU5r0wqXxkjsOoDWfhyS8ZMbCI9LrhHmu/aUz6ZPFqO6ttVNm7TUQ4YPiHhi9YiLy/8QFaaWsyWa/pusdod0bh4tpE263WXk6ctal3HRVdJ3y+v1yrdel1Plmkm1XJZvHCBBJ5o/XzRXytin1v08kJZHCZziuaZ8GJkfWweCbGxyX2fi67pK1+2eJrPjaTryb/zpVj3aznPrJtL/JVVixfKy1GNtWiBLFy8Ij4jUrTbQy54ZKbctefHMnnkKdK365elTZuDZPiEGTI/dLBIlnWlUqmgrxSy9ZRv281lu1065qBG7aVLn/4yePRU8bzl0jJrnBy6+Abp2/tqmRHUGNfh9v+3c34hbV1hAP95A9aHJhuugokPLSNoCnOMxcmgBWNckwkdSIZlD0qt0IXRxkKnCxW3wZIKjaUloA+jKDpFcKBMfCgdw9mBD5W4F2VNhvgwRN3bHkI3ZNVxb25Sk3vzrzgUewIhybnnfH9+5+Twne/ccxORqkEpb2U49recttS8N+84MSXbuoaJybcsaurJt4pWUXnGijlZt+DP0rzttJFxwcJzV8zpT+LWVyiQjUaTGdfwU55rWO2xt9mP06Q31bxMG43iggqkyjO8k6uzNKu3PGJPVuP0XOXOz5vsPd8kMn2B7b4mHIEFjmJ8r0c/j4fi8qtHoJw6twuzZnkbZyO2fkg4SjHbW/j08keY06KxdWIb+5M6u8Q31lgxu3DXncJU9wHt5qcsrv6ZfvgovsTdRivuEflQUtLfX1nd2h/l7RJfvk+jchhqR5WVRV9WKlIOGzaJrUBtjYX9yaCsogq+UIw/+djoKDW9jbvdwsrib2ylrUT+YvnuRf1DXAW1KcN6/kNcZDDejTLitujL1TFPKcqqTx3DmrRkNkE65ZIZu6eDy+12/rfVmI7aYorERF8MrVe2roTJ4WWweY423zhRZXkqn9q8RyC0fABU9uf6/yEe/1crU/lzW2n0z7xYHsd/56dHy9D5CW5rmdpmmVDgHjNK3nSXeHQcX9sczYNeHHJUaTpP12ADD69/RXhpKzHZx6PMBL6kh2v0X6pGIunvY673PmBJmezlE5g/EOgegoFuLlWXqbLeZ7zNz0hUjuMSdW4HRnOndEx1XAnWZ9iwyojvBqGaHtUGLYKXLynGn3xs9Kw4haOrl+aHX9MbXlQne3l8hOjugYF+j84hrsLaSFY3/ltvEAoMMa/0ww5bC1OM//iuKreAsaOYXE79FR8XMmyMjvhpC1VmsVHPV0ic8HXjn4mqeylyv//CoyXo9DZhPYKz6hE0SR+uKD1kAtJpPOFpxmrncRrlvLUN75Oz+AZaDsCwMqzNV7m100eN4U0+/n4tPdqWNUg2Okan8FXM4lD0l1BibGW2wstc8CJVqZHs4ov2s6zfPkdJiQGjc57asWnCntPq5mspVZ5+FiYa2PbbMci5ZFVOZPIa9uRms+rvRMMf+C0nErIcs1T4ppi8Wa9G3Kqssbd47JTztAaM3gjv+bpw5aRiwtZ5P8OGz4k1hInN3XhhQ04ZRV4sxp98bHRUS1UthBfCNGx/g8UgP9riNRyz5fgiD7hpf12nBRTURqrCGRwl0vGMgNIPJ7AEntGRkqsdO4l9mEyVEidt7Qyl2Wjjs9g5JmKTdGexMVOK/FuqbmM04qVithWjshdhwKiMjW8JtiTHmV7LwysTz6M/PPZC84ESkJ8x04etaY1g7Ds65YhbvAQBQUAhkIqDBA9BQBAQBASB40lATPTHs1+FV4KAICAIpAiI1E0KhfgiCAgCgsDxJCAi+uPZr8IrQUAQEARSBP4Dc6KDAMBtE24AAAAASUVORK5CYII="></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Define <em>frame of reference.</em></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In the reference frame of the laboratory the force on X is magnetic.</p>
<p>(i) State the nature of the force acting on X in this reference frame where X is at rest.</p>
<p>(ii) Explain how this force arises.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>This question is about special relativity, simultaneity and length contraction.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>One of the two postulates of special relativity may be stated as:</p>
<p style="padding-left: 30px;">“The laws of physics are the same for all observers in inertial reference frames.”</p>
<p>State</p>
<p>(i) what is meant by an inertial frame of reference.</p>
<p>(ii) the other postulate of special relativity.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In a thought experiment to illustrate the concept of simultaneity, Vladimir is standing on the ground close to a straight, level railway track. Natasha is in a railway carriage that is travelling along the railway track with constant speed <em>v</em> in the direction shown.</p>
<p><img 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" alt></p>
<p>Natasha is sitting on a chair that is equidistant from each end of the carriage. At either end of the carriage are two clocks C<sub>1</sub> and C<sub>2</sub>. Next to Natasha is a switch that, when operated, sends a signal to each clock. The clocks register the time of arrival of the signals. At the instant that Natasha and Vladimir are opposite each other, Natasha operates the switch. According to Natasha, C<sub>1</sub> and C<sub>2</sub> register the same time of arrival of each signal.</p>
<p>Explain, according to Vladimir, whether or not C<sub>1</sub> and C<sub>2</sub> register the same time of arrival for each signal.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The speed <em>v</em> of the carriage is 0.70c. Vladimir measures the length of the table at which Natasha is sitting to be 1.0 m.</p>
<p>(i) Calculate the length of the table as measured by Natasha.</p>
<p>(ii) Explain which observer measures the proper length of the table.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>When a spaceship passes the Earth, an observer on the Earth and an observer on the spaceship both start clocks. The initial time on both clocks is 12 midnight. The spaceship is travelling at a constant velocity with <em>γ</em> = 1.25. A space station is stationary relative to the Earth and carries clocks that also read Earth time.</p>
</div>
<div class="specification">
<p>Some of the radio signal is reflected at the surface of the Earth and this reflected signal is later detected at the spaceship. The detection of this signal is event B. The spacetime diagram is shown for the Earth, showing the space station and the spaceship. Both axes are drawn to the same scale.</p>
<p style="text-align: left;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the velocity of the spaceship relative to the Earth.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The spaceship passes the space station 90 minutes later as measured by the spaceship clock. Determine, for the reference frame of the Earth, the distance between the Earth and the space station.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>As the spaceship passes the space station, the space station sends a radio signal back to the Earth. The reception of this signal at the Earth is event A. Determine the time on the Earth clock when event A occurs.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Construct event A and event B on the spacetime diagram.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate, using the spacetime diagram, the time at which event B occurs for the spaceship.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>This question is about relativistic kinematics.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by an inertial frame of reference.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A spaceship travels from space station Alpha to space station Zebra at a constant speed of 0.90c relative to the space stations. The distance from Alpha to Zebra is 10ly according to space station observers. At this speed <em>γ</em>=2.3.</p>
<p><img 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" alt></p>
<p>Calculate the time taken to travel between Alpha and Zebra in the frame of reference of an observer</p>
<p>(i) on the Alpha space station.</p>
<p>(ii) on the spaceship.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain which of the time measurements in (b)(i) and (b)(ii) is a proper time interval.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The spaceship arrives at Zebra and enters an airlock at constant speed. O is an observer at rest relative to the airlock. Two lamps P and Q emit a flash simultaneously according to the observer S in the spaceship. At that instant, O and S are opposite each other and midway between the lamps.</p>
<p><img 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" alt></p>
<p>Discuss whether the lamps flash simultaneously according to observer O.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>This question is about relativistic kinematics.</p>
<p>Speedy is in a spacecraft being chased by Police Officer Sylvester. In Officer Sylvester’s frame of reference, Speedy is moving directly towards Officer Sylvester at 0.25c.</p>
<p><img 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" alt></p>
<p> </p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe what is meant by a frame of reference.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>At a later time the police spacecraft is alongside Speedy’s spacecraft. The police spacecraft is overtaking Speedy’s spacecraft at a constant velocity.</p>
<p>Officer Sylvester is at a point midway between the flashing lamps, both of which he can see. At the instant when Officer Sylvester and Speedy are opposite each other, Speedy observes that the blue lamps flash simultaneously.</p>
<p><img 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" alt></p>
<p>State and explain which lamp is observed to flash first by Officer Sylvester.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The police spacecraft is travelling at a constant speed of 0.5c relative to Speedy’s frame of reference. The light from a flash of one of the lamps travels across the police spacecraft and is reflected back to the light source. Officer Sylvester measures the time taken for<br>the light to return to the source as 1.2 × 10<sup>–8</sup>s.</p>
<p>(i) Outline why the time interval measured by Officer Sylvester is a proper time interval.</p>
<p>(ii) Determine, as observed by Speedy, the time taken for the light to travel across the police spacecraft and back to its source.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>This question is about relativistic kinematics.</p>
<p>A spacecraft leaves Earth and moves towards a planet. The spacecraft moves at a speed 0.60c relative to the Earth. The planet is a distance of 12ly away according to the observer on Earth.</p>
<p><img 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" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the time, in years, that it takes the spacecraft to reach the planet according to the</p>
<p>(i) observer on Earth.</p>
<p>(ii) observer in the spacecraft.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The spacecraft passes a space station that is at rest relative to the Earth. The proper length of the space station is 310 m.</p>
<p>(i) State what is meant by proper length.</p>
<p>(ii) Calculate the length of the space station according to the observer in the spacecraft.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>F and B are two flashing lights located at the ends of the space station, as shown. As the spacecraft approaches the space station in (b), F and B turn on. The lights turn on simultaneously according to the observer on the space station who is midway between the lights.</p>
<p><img 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" alt></p>
<p>State and explain which light, F <strong>or</strong> B, turns on first according to the observer in the <strong>spacecraft</strong>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>This question is about relativistic kinematics.</p>
<p>In a thought experiment, a train is moving at a speed of 0.950c relative to the ground. A pendulum attached to the ceiling of the train is set into oscillation.</p>
<p><img 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" alt></p>
<p>An observer T on the train and an observer G on the ground measure the period of oscillation of the pendulum.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State and explain whether the pendulum period is a proper time interval for observer T, observer G <strong>or</strong> both T and G.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Observer T measures the period of oscillations of the pendulum to be 0.850s. Calculate the period of oscillations according to observer G.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Observer T is standing in the middle of a train watched by observer G at the side of the track. Two lightning strikes hit the ends of<br>the train. The strikes are simultaneous <strong>according to observer T.</strong></p>
<p><strong><img 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" alt></strong></p>
<p> </p>
<p>Light from the strikes reaches both observers.</p>
<p>(i) Explain why, according to observer G, light from the two strikes reaches observer T at the same time.</p>
<p>(ii) Using your answer to (i), explain why, according to observer G, end X of the train was hit by lightning first.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>An observer P sitting in a train moving at a speed <em>v</em> measures that his journey takes a time Δ<em>t</em><sub>P</sub>. An observer Q at rest with respect to the ground measures that the journey takes a time Δ<em>t</em><sub>Q</sub>.</p>
</div>
<div class="specification">
<p>According to Q there is an instant at which the train is completely within the tunnel.</p>
<p>At that instant two lights at the front and the back of the train are turned on simultaneously according to Q.</p>
<p style="text-align: center;"><img 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"></p>
<p>The spacetime diagram according to observer Q shows event B (back light turns on) and event F (front light turns on).</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-09-26_om_14.55.20.png" alt="M17/4/PHYSI/SP3/ENG/TZ1/4d_02"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State which of the two time intervals is a proper time.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the speed <em>v</em> of the train for the ratio \(\frac{{\Delta {t_{\text{P}}}}}{{\Delta {t_{\text{Q}}}}} = 0.30\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Later the train is travelling at a speed of 0.60c. Observer P measures the length of the train to be 125 m. The train enters a tunnel of length 100 m according to observer Q.</p>
<p>Show that the length of the train according to observer Q is 100 m.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the time \(ct'\) and space \(x'\) axes for observer P’s reference frame on the spacetime diagram.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce, using the spacetime diagram, which light was turned on first according to observer P.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Apply a Lorentz transformation to show that the time difference between events B and F according to observer P is 2.5 × 10<sup>–7</sup> s.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Demonstrate that the spacetime interval between events B and F is invariant.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.iv.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A second train is moving at a velocity of –0.70c with respect to the ground.</p>
<p style="text-align: center;"><img 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"></p>
<p>Calculate the speed of the second train relative to observer P.</p>
<p> </p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>An observer on Earth watches a rocket A. The spacetime diagram shows part of the motion of A in the reference frame of the Earth observer. Three flashing light beacons, X, Y and Z, are used to guide rocket A. The flash events are shown on the spacetime diagram.<br>The diagram shows the axes for the reference frames of Earth and of rocket A. The Earth observer is at the origin.</p>
<p><img 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" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For the reference frame of the Earth observer, calculate the speed of rocket A in terms of the speed of light <em>c</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using the graph opposite, deduce the order in which</p>
<p>(i) the beacons <strong>flash</strong> in the reference frame of rocket A.</p>
<p>(ii) the Earth observer <strong>sees</strong> the beacons flash.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br>