Relativistic Energy and four momentum

[golfingboy07]

A particle of initial kinetic energy T0 and rest energy E0 strikes a like particle at rest. The initial particle is scattered at an agle theta to its original direction. Show that the final kinetic energy T is

T = T0cos2(theta)/(1+ (T0sin2(theta)/2E0))

what I have so far:

We know that T = E - E0 and that four momentum will be conserved. Also I think if we choose a suitible invariant it may simplify the problem

Could I get more suggestions/hints a starting point etc.

Thanks

GM

 

[quasar987]

The total energy before and after the collision is the same, as well as the total linear momentum, so I suggest you start by writing those 3 "conservation equations" (1 for energy, 1 for x-component momentum and 1 for y-component momentum)