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

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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. Part of written assignment: 14. [4pt] Draw two Minkowski space-time diagrams, covering the stretch of time from a little before the superglue is disolved, to a little after both members of the dynamic duo have hit the ground. Include labeled worldlines for Batman (B), Robin (R), the Joker (J), and a telephone pole in the ground (T). The telephone pole zooms past them all just as Batman and Robin start running. One of the diagrams should be from the Joker's perspective (that is, Joker's world line is vertical), and the other should be fron the telephone pole's perspective. ONLY for this drawing: Instead of the values above, use the following: train speed is 0.25c, dynamic duo speeds are 0.6c relative to the train, and they run for 50 ns on their own watches. The diagrams should be quantitatively correct, including scales on the perpendicular axes. Hints: Although the speed transformation equation can be useful here, it is easier to transform events. Note that the problem does not require coordinate axes other than the perpendicular set. Indeed, since Batman and Robin change velocities, they don't even have a single coordinate system for the whole scenario.

Explanation / Answer

en.wikipedia.org/wiki/Minkowski_diagram chect it

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