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: