Aeighme
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Homework Statement
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 = 0.64c 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. Fortunately, Batman remembered to pack 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 = 0.74c, measured in the frame in which the train is at rest. They each run for a time Δt' = 19.3 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 member of the Dynamic Duo is hurt.
According to the Joker, who is at rest with respect to the train, how far apart are Batman and Robin when they jump?
Homework Equations
t=t1*gamma
d=vt
The Attempt at a Solution
I tried finding the Joker's measured time and then calculated the distance..but it didn't work..nor did it seem right.