In working problems on Collision or Impact, the following method is often useful:

Imagine a rigid plane moving with velocity equal to that of the centre of gravity of two bodies, so that during collision it touches and separates the surfaces of contact. (We may either suppose that the mass of the plane is infinite, or that it is constrained to move as stated.) Then the motions of the two bodies due to their mutual impact will obviously be the same as if each separately had impinged on this plane. Thus the problem of two bodies is reduced to two simpler problems of one body impinging on a body whose motion is fixed. And we may by giving to each of the bodies in question, in addition to its own motion, a motion equal and opposite to that of the centre of gravity of the system, bring the plane of impact to rest, so that the motion of each body relative to this plane is the same as that of a body impinging on a fixed body.