What is the rest mass of the composite particle after a relativistic collision?

[Void123]

Homework Statement

A stationary particle of rest mass [tex]2m_{0}[/tex] is hit by a particle of rest mass [tex]m_{0}[/tex] and kinetic energy [tex]2m_{0} c^{2}[/tex]. I must find the rest mass of the composite particle afterward.

Homework Equations

Conservation of momentum and energy.

The Attempt at a Solution

I worked problems with identical mass and velocity, but I don't exactly know what to do with this particular problem. I'm still having trouble understanding the explanation my book provided, so I was hoping someone can give me a more lucid elaboration of this whole phenomenon.

 

[Void123]

This is what I have so far.

[tex]m_{0} \gamma (u) u = M_{0} q \gamma(q)[/tex]

[tex]m_{0} \gamma (u) + 2m_{0} = M_{0} \gamma (q)[/tex]

[tex]M_{0}[/tex] is the rest mass of the composite particle, [tex]q[/tex] its velocity, and [tex]u[/tex] the velocity of the inertial particle before it strikes the stationary one.

The problem is the ratio [tex]\frac{M_{0}}{m_{0}}[/tex], which is what I need, is eliminated.

I don't know where to proceed from here.