1. The problem statement, all variables and given/known data Consider a head-on, elastic collision between two bodies whose masses are m and M, with m << M. It is well known that if m has speed v0 and M is initially at rest, m will bounce straight back with its speed unchanged, while M will remain at rest (to an excellent approximation). Use this fact to predict the final velocities if M approaches with speed v0 and m is initially at rest. 2. Relevant equations u = u' + v (the classical velocity addition formula) Newton's Second Law: F = ma & F' = m'*a' (The two laws for the two fixed reference frames S and S') 3. The attempt at a solution Basically, the way I would solve this problem is think that m and M are both masses. Since u = u' + v and u' = u - v, using Newton's First Law, small m is isolated from all outside forces so then the velocity u is constant relative to the lab. Then the velocity of M is going to be v0.