Help with Energy at inelastic collision

[FLms]

Homework Statement

A particle of mass m₁ and momentum p₁ collides with a particle of mass m₂ at rest. A reaction occurs, as a result giving two new particles, with masses m₃ and m₄, that are emitted at angles
[itex]\theta_3[/itex] and [itex]\theta_4[/itex], in relation to the original direction of m₁. Determine the energy Q that has been produced on the reaction in terms of the masses, the angles and p₁.

Homework Equations

[tex]Q = T_f - T_i[/tex]
[tex]T = \frac{p^2}{2 m}[/tex]

The Attempt at a Solution

[tex]p_1 = p_3 cos(\theta_3) + p_4 cos(\theta_4)[/tex]
[tex]p_2 = 0 = p_3 sin(\theta_3) - p_4 sin(\theta_3)[/tex]
[tex]Q = T_3 + T_4 - T_1[/tex]
[tex]Q = \frac{{p_3}^2}{2m_3} + \frac{{p_4}^2}{2m_4} - \frac{{p_1}^2}{2m_1}[/tex]

I'm stuck here.
I suppose I have to, obviously, express both [itex]p_3[/itex] and [itex]p_4[/itex] in terms of [itex]p_1[/itex], but I'm not exactly sure of how to do it. Or maybe I just need some algebraic manipulation to get rid of both [itex]p_3[/itex] and [itex]p_4[/itex].

Any help appreciated.

 

[ojs]

That absolutely correct, you need algebraic manipulation to express [itex]p_3[/itex] and [itex]p_4[/itex] in terms of [itex]p_1[/itex], [itex]\theta_3[/itex] and [itex]\theta_4[/itex].

 

[Redbelly98]

... and these are the equations you need to manipulate:

[tex]p_1 = p_3 cos(\theta_3) + p_4 cos(\theta_4)[/tex]
[tex] 0 = p_3 sin(\theta_3) - p_4 sin(\theta_3)[/tex]