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Elastic Collision: Relative velocity

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Consider a head-on elastic collision between two particles. (Since the collision is head-on, the motion is confined to a single straight line and is therefore one-dimensional.) Prove that the relative velocity after the collision is equal and opposite to that before. That is, v_1-v_2= -(v'_1-v'_2), where v_1 and v_2 are the initial velocities and v'_1 and v'_2 the corresponding final velocities.

I understand inelastic collisions but not elastic. Outline of solution please.

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Solution Summary

The relative velocity of the particles before and after collision are compared.

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