I need help with problem R2R4 in Six Ideas that Shaped Physics Unit R A train is

Question

I need help with problem R2R4 in Six Ideas that Shaped Physics Unit R

A train is moving due east at a large constant speed on a straight track. Suppose that Harry is riding on the train exactly halfway between its ends. Sally is sitting by the tracks only a few feet from the train. Let the event of Harry passing Sally be the origin event O in both frames. At this same instant, both Harry and Sally receive the light from lightning ashes that have struck both ends of the train, leaving scorch marks on both the train and the track. Harry concludes that since he is in the middle of the train and he received the light from the strikes at the same time, the lightning strikes must have occurred at the same time in his reference frame. Is he right? If not, which strike (the one at the front of the train or the one at the rear) really happened rst? Can Sally conclude from her seeing the ashes at the same time that the strikes happened at the same time in the ground frame? If not, which strike happened rst in her frame? (This problem is adapted from one of Einstein’s own illustrations of the implications of the frame-independent speed of light.) Note: Five questions are to be answered and step by step solutions are appreciated

Explanation / Answer

First of all, let us review what the problem tells us:

1. Harry is in a moving frame while Sally is in a stationary frame (assuming the earth to be stationary with respect to the velocity of the train)

2. At the origin, the lighting falls on both ends of the train.......this event is judged from Sally's frame and Harry frame.

Let A = Rear end of train where lightning strike occurs and B = Front end of train where lightning strikes

Harry moves east wards with a "large" velocity. So, he is always approaching B, while gaining an increasing distance from A. So it will be a (d/2 - vt) relative distance of appraoch for B, while the relative distance of appraoch will be (d/2 + vt) for pt A if we assume the train has velocity v and it moves for time t.

Hence, in Harry's frame, the light from B will always approach Harry faster than the light from A. He will see that front end strike happened first.

However, Sally is in a frame relatively at rest with respect to Harry. Since at the origin, the lighting strikes A and B simultaneously, she will conclude both events are simultaneous. For Sally, the relative distance between A and B to her position remain the same.

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