Two trains, A and B, each have proper length l, and both move in the positive x direction. Relative to the lab frame, train A travels at speed 4c/5, and train B at speed 3c/5. Train A starts behind B.

Let event E1 be the moment that the front of train A passes the back of train B. And let event E2 be the moment that the back of train A passes the front of train B.

(a) As viewed by an observer, C, in the lab frame, how long does train A take to overtake train B? (That is, what is the observed duration between events E1 and E2?)

(b) Sketch the above situation in a space-time diagram, clearly indicating E1 and E2.

(c) How long, as viewed by an observer at rest in train A, does it take for A to overtake B?

(d) Without calculation, how long does the overtaking process take for an observer at rest in train B? Justify your answer.

(e) Alice walks at constant speed, v0, in train B from the back to the front. She leaves the back of the train at the moment of event E1, and reaches the front of the train at the moment of event E2.

i. At what speed is she walking? ii. How long does the overtaking process take from her point of view?