Standard collision examples Development of equations Elastic vs Inelastic
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Head-on Elastic Collisions, Target at Rest

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:

Note that these equations apply only to the case where the target is at rest.

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Elastic collisions, target at rest Standard examples, elastic collisionsCalculation for headon case.
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Velocities After Collision

For head-on elastic collisions where the target is at rest, the derived relationship

may be used along with conservation of momentum equation

to obtain expressions for the individual velocities after the collision.

These relationships may be used for any head-on collision by transforming to the frame of the target particle before using them, and then transforming back after the calculation. However, one may calculate the case for head-on collisions where both particles are moving with the relationships:

Calculation for headon case.
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Collision concepts

Elastic collisions
 
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