4. You have a twin that stays at home on the Earth while you travel in a spaceship. You leave Earth when you and your twin are both 20.0 years old. You travel from Earth in a straight line at a constant speed for 2.50 years in your frame and you return to Earth in a straight line at the same speed, so that your total travel time in your frame is 5.00 years (assume that the acceleration times are zero). When you return to Earth, you are 12.0 years younger than your twin (biological age). a. What is your twins age when you return to Earth? b. What is the speed parameter of your spaceship for this trip, ß = v/ c ? c. How far from Earth (as measured in the Earth frame) did you travel before turning around (give the answer in light years (ly ) in the Earth frame - hint the speed parameter tells you the speed in units of light years per year)?

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Which of the following is true about time dilation?A. The time measured by a moving observer increases.B. The time measured by the ground observer increases.C. The time measured by the ground observer decreases.D. The time measured by the moving observer equals time measured by the ground observer.

Identify the postulates of special theory of relativity that apply in the following situations. 1. The ball appears to move north at a speed of around 2 m/s and then south at a speed of 2m/s. 2. A planet’s orbit is measured relative to the star it is orbiting around.

2. You boarded a space craft that moves at half the speed of light, if to an observer on the earth you appear to be 5.5 m tall as you travel, how tall are you when you are at rest on the earth?

1. Firecrackers and rockets: Suppose a rocket pilot sets off two firecrackers, the second exactly 10 days after the first (according to the pilot). Now suppose that according to an observer on Earth, the rocket is moving at a constant speed v and the two firecracker-explosions are spatially separated by Ar = 2 - 1014m, i.e. that the rocket travels a distance Ax between the explosions. How much time passed on Earth between these explosions? Relativistic velocity addition: Consider a universe in which Einstein's postulates and special ilog (hour imstead of 3- 10°m/s. A Cessna 2. 0000

1. Consider inertial reference frame S to be the lab frame. A proton is moving in the positive x (+x) direction at a kinetic energy of 1250 MeV, as measured in frame S. Inertial reference frame S' moves at a speed of 0.55c in the positive-x (+x) direction relative to frame S. a) Find the speed of the proton in terms of the speed of light, c, as measured in frame S. b) Find the magnitude and direction of the speed of the proton as measured in frame S'.

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Two events that happen at different positions x1 and x2 but at the same time t1 = t2, as measured in some reference frame, are said to be

1 2. Preparations are under way for a spacecraft visit to the Alpha Centauri star system, 4.30- lightyears away Provisions are placed on board to allow for a trip of 8 years. a. What minimum speed must the spacecraft travel relative to Earth if the provisions are to last?