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(9.0.6) A train car of unknown length moving at unknown speed v passes a platfor

ID: 2104688 • Letter: #

Question

(9.0.6) A train car of unknown length moving at unknown speed v passes a platform with a rest length of 80 m. Observers A and B stand at opposite ends of the platform and have synchronized watches. Observers A’ and B’ stand at opposite ends of the train car, playing catch with each other, and have synchronized watches. Observer A notes that at time t = 0, the end of the train car coincides exactly with his position, and sees that watch worn by passenger A’ reads 0s. Observer B notes that at time t = 0, the front of the train car coincides exactly with his position, and that the watch worn by B’ reads -150 ns. (B’ has a watch which gives negative times.)

(a) How fast is the train moving? (b) How long is the train car? (c) At the same time that the positions of A and A’ coincide, A’ throws a ball to B’ at

2.00×108 m/s as measured by the train observers. Find the time at which the ball is caught in the train frame. (d) Find the time and position at which the ball is caught as measured in the platform frame. Take the position of A to be the origin of the platform frame.

Explanation / Answer

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