A train with proper length L moves at speed 4c/5 with respect to the ground. A...

A train with proper length L moves at speed 4c/5 with respect to the ground. A ball is thrown from the back to the front, at speed c/3 with respect to the train. How much time does this take, and what distance does the ball cover, in:

(a) The train frame?
(b) The ground frame? Solve this by
i. Using a velocity-addition argument, as we did in lecture.
ii. Using the Lorentz transformations to go from the train frame to the ground frame.
(c) The ball frame?
(d) Verify that the invariant interval is the same in all three frames.
(e) Show that the times in the ball frame and ground frame are related by the relevantγ factor.
(f) Ditto for the ball frame and train frame.
(g) Show that the times in the ground frame and train frame are not related by therelevant γ factor. Why not?
(h) Show that the time in the ground frame is related by the relevant γ factor to the time that elapses on a given clock on the train, as viewed from the ground. (The rear-clock-ahead effect will come into play.)

Solutions

Expert Solution

genius_generous answered 1 year ago

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