Consider the collision of two particles, one of massmoving with speed u which collides head on with a particle of
at rest in its own inertial frame O', relative to which particle 1 has speed
along the positive x axis. Having particle 2 at rest in its own inertial frame makes the solution simpler, and the speed of each particle in any other inertial frame can be found using the velocity transformations.
Before Collision
After Collision
Conservation of momentum gives
(3)
(4)
Conservation of energy gives(5)
Since(6) we have
Ifand
then from (4),
then from (5) that
(7)
Putand
in (3) to obtain
From (7) then we obtain
Hence