Physics 200 Homework 3, Part Two Due at the end of class, Wed Sept 30th Don't forget to complete Part One, on Connect! 1. Summative question for the on-line homework (a) Assume that the second ship from the on-line homework is moving at 0.25c in the direction opposite from the first ship. What is its speed as viewed from the first ship's frame of reference now? (Write up your solution, don't just state the answer. The calculation is almost identical to the one you did in the online homework. You will get no credit if you use the addition of velocities formula on this part.) (b) Check your answer for question (a) above using the addition of velocities formula. 2. Laser guns on a train A long train is moving at speed 0.6c. Let L denote the length of the train. Ann and Josie are standing on two ends of this train, Ann at the back and Josie at the front. One- quarter of the way from the back of the train there is a target. Ann and Josie both fire their laser guns at the target; their two short blasts hit the target at the same time. (a) Consider the two events 'Ann fires her gun' and 'Josie fires her gun'. How far apart are these two events in the train's frame of reference? (b) In the frame of the train, who fired their gun first and by how much? (express your answers in terms of L/c). (c) In the frame of the ground, who fired their gun first and by how much? (Use Lorentz Transformations for full marks.) (d) How far apart are these two events in the stationary frame of reference? Try to answer this question in two ways: (i) Not using the LT (ii) Using the LT and your answers to a, b and c. Turn over for one more question ... 1
3. Left and Right The Earth lies midway between two stars, Left and Right, with 3 light years separating the Earth from each of these two stars. A spaceship travelling at a speed \3c from Left to Right flies over the Earth. When the spaceship is halfway between Earth and Right (all in the stationary frame of reference), Right experiences a violent solar flare. In the ship's frame of reference, how far is the ship from the Earth when the solar flare occurs? Is it closer to Right or to Left then? 2