Physics 200 Homework 2, Part Two Due at the end of class, Wed Sept 23rd Don't forget to complete Part One, on Connect! You should complete the questions below using relativistic physics. 1. Passing Trains Two trains, A and B, are going in opposite directions on two parallel tracks. Define passing time to be the length of time from the moment when the fronts of the trains are lined up to the moment when the backs of the trains are lined up. (a) Assume that the two trains are identical (have the same length). Argue, using the Principle of Relativity, that the passing time is the same when viewed from A's frame of reference as it is from B's frame of reference. (b) Let train A be twice the length of train B. If the passing time in A's frame of reference is 50% longer than the passing time in B's frame of reference, what is the relative speed v of the two trains? Give your answer in the form 'number x c'. Hint: solve for y first, then square it and solve for v. 2. Interstellar trips Aidan and Nadia are twins. When they turn 21, they decide to have an adventure. Aidan chooses to travel to a star 10 light years away on a ship whose speed is 0.8c. Nadia chooses to travel to a slightly closer star, 8 light years away. How fast must Nadia's ship travel to and from the closer star so that the two twins are still the same biological age after they both return to Earth? (They won't necessarily return at the same time. ) but will be the same age as each other for the rest of their lives on Earth). 1