Holy Time Dilation! The Joker has captured Batman and Robin and has superglued t

Question

Holy Time Dilation! The Joker has captured Batman and Robin and has superglued them together to the roof of a train, which is moving at a steady velocity of magnitude v = 0.65c toward a low bridge. Confident that his diabolical plan will finish off the Dynamic Duo for good, the Joker returns to his seat in the train (directly beneath where they are stuck). Fortunately, Batman has packed some super-bat-glue-solvent in his utility belt, and is able to apply the solvent to the superglue. At the instant they are freed, the superheroes simultaneously set their stop watches to zero, and then (by pre-arrangement) they start running along the train in opposite directions at speed u = 0.76c, measured in the frame in which the train is at rest. They each run for a time ?t' = 21.9 ns, as measured on their own stop watches, and then they each jump from the train, just before the train passes under the bridge. They hit the ground with a sharp thud, and come instantly to a stop. Miraculously, neither of our heros is hurt. 15. [3pt] According to the Joker, who is at rest with respect to the train, how far apart are Batman and Robin when they jump? Answer: 16. [3pt] As measured on the ground, how far apart are the two points at which the pair hit the ground? Answer: 17. [3pt] As seen from the ground, what is the time difference between the two thuds? Answer:

Explanation / Answer

u=(u1+v)/(1+(u1/c2))

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