Running on a train **
A train of proper length L moves at speed v1 with respect to the ground. A passenger runs from the back of the train to the front at speed v2 with respect to the train. How much time does this take, as viewed by someone on the ground? Solve this in two different ways:
(a) Find the relative speed of the passenger and the train (as viewed by someone on the ground), and then find the time it takes for the passenger to erase the initial ``head start'' that the front of the train had.
(b) Find the time elapsed on the passenger's clock (by working in whatever frame you want), and then use time dilation to get the time elapsed on a ground clock.