Consider a one-dimensional, head-on elastic collision. One object has a mass m1 and an initial velocity v1; the other has a mass m2 and an initial velocity v2. Use momentum conservation and energy conservation to show that the final velocities of the two masses are

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2m2 (m, - т, v, + т, + mz + m2 2m, т, + mz, т, 'm, — т, V2 v, + т, + mz, тz.