I've been having some difficulty with the problem described below, please have a look:
Two particles with identical masses (m) undergo a collision. Before the collision they move with velocities (c/2,0,0) and (-c/2,0,0), and after the collision, they move with velocities (0,c/2,0) and (0,-c/2,0) in frame S.
How can I find the velocity of the particles AFTER the collision in frame S' where one of the particles is at rest prior to collision??
Working so far: Using the RELATIVISTIC SPEED ADDITION FORMULA for the normal x-axis case, I have obtained $u'x=4/5c$ for the particle not at rest BEFORE the collision. HOW DO I SOLVE THE PROBLEM FOR THE Y-AXIS CASE AFTER THE COLLISION IN THE S' FRAME?
Also, how can I show there is a conservation of momentum before and after collision using the formula p=(gamma)mv? The different direction of velocity after the collision is confusing me...since momentum is conserved linearly right?
A detailed description would be appreciated!
THANK YOU SO MUCH! :)