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Head-on Elastic Collisions

Conservation of momentum
Conservation of kinetic energy

To obtain expressions for the velocities after the collision, rewrite the above as:

Dividing these relationships gives

which may be substituted into equation (2) above to obtain:

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Velocities After Collision

For head-on elastic collisions , the derived relationship

may be used along with conservation of momentum equation

to obtain expressions for the individual velocities after the collision.

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