How to Calculate Energy Produced from Collision of Particles?

[1missing]

Homework Statement

A particle of mass m₁ and momentum p₁ collides with a particle of mass m₂ at rest. A reaction occurs from which two particles of masses m₃ and m₄ leave the collision along the angles θ₃ and θ₄ respectively, measured from the original direction of particle 1. Find the energy Q produced by the reaction in terms of the masses of the particles, the angles, and p₁.

Homework Equations

p_i = p_f Conservation of momentum

KE_i = KE_f + Q Conservation of energy

The Attempt at a Solution

To be honest I'm having the hardest time just making sense of the problem. I feel like I'm missing something. Do particles 1 and 2 still exist after the collision? Do they rebound? Do they stick together? Does it even matter if I'm just trying to find Q? Really not sure what the heck is going on.

 

[Orodruin]

Do particles 1 and 2 still exist after the collision?

If they did, this would be mentioned in the problem statement. Hence, they do not.

 

[1missing]

Does m₂ even enter the problem then?

 

[Orodruin]

Yes. You will need it to be able to uniquely identify the energies and momenta of the outgoing particles.

 

[Orodruin]

Wait, is this a classical or a relativistic problem?

 

[1missing]

I'm assuming it's a classical problem because we haven't done anything relativistic all semester, which leads me to the question of where does m₂ enter into the problem? It's at rest, so no initial momentum and no initial kinetic energy, and the particle doesn't exist after the collision, so should I be considering the rest energy of the particles?

Edit: Nevermind, think I solved it without the need for m₂.

 

[haruspex]

should I be considering the rest energy of the particles?

Yes.

think I solved it without the need for m2.

I don't see how. Please post your working.