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Take the general case of a body of mass m1 and velocity v1 elastically striking a stationary (v2-0) body of mass m2 head-on. Show that the final velocities v1 and v2 are given by....
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Apply conservation of momentum and then conservation of kinetic energy. You get two equations in v1 and v2. Solve them. The math may be a bit tedious, but that's all. It is a fairly simple case.
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