A train moves due east on a straight track at a constant speed of 20m s−1. A passenger starts walking inside the train toward the locomotive at a constant speed of 1.5m s−1 measured with respect to the train.
(i) At t=0, the locomotive passes a station S that is chosen as xG=0 in the ground frame G. At the same instant the passenger is 10m behind the locomotive, so that his coordinate in the train frame T is xT=−10m. Write an algebraic relation connecting xG and xT.
(ii) Using the relation from part (i), obtain an explicit expression xG(t) for the position of the passenger in the ground frame as a function of time.
(iii) Find the passenger’s coordinates in both frames after 12s have elapsed.
(iv) Differentiate your result in part (ii) to obtain the passenger’s velocity with respect to the ground and show that it equals the vector sum of the train’s velocity and the passenger’s walking velocity.