Hi guys, I've been thinking on a problem for a while which really bothers me. I've been trying to mathematically solve the following problem: A train approaches the station at a velocity of V=50 m/s. Then a tennis ball is thrown with a velocity U=30 m/s, against the approaching train. Assume that the collision is absolutely elastic. If the train's velocity after the collision is V=50 m/s, then what is the speed of the ball with respect to the train station? So, here is my approach to the problem: From the momentum conservation law and the fact that the train will have the same momentum after the collision, we can write: MtrainV - mballU = MtrainV + mballUfinal so it turns out that the velocity of the ball will be: Ufinal = - U = -30 m/s Which is incorrect. The correct answer should be: Ufinal = 2V+U = 130 m/s Can someone provide a rigorous derivation of the later equation? Your help will be highly appreciated!