A boy on a train of height `h_1` projects a coin his friend of height `h_2` standing on the same train, with a velocity `v` relative to the train, at an angle `theta` with horizontal. If the train moves with a constant velocity `v'` in the direction of x - motion of the coin, find the
(a) distance between the boys so that the second boy can catch the coin,
(b) maximum height attained by the coin, and
( c) speed with which the second boy catches the coin relative to himself (train) and ground.