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## Homework Statement

A particle of mass

*m*and momentum

_{1}*p*collides with a particle of mass

_{1}*m*at rest. A reaction occurs, as a result giving two new particles, with masses

_{2}*m*and

_{3}*m*, that are emitted at angles

_{4}[itex]\theta_3[/itex] and [itex]\theta_4[/itex], in relation to the original direction of

*m*. Determine the energy

_{1}*Q*that has been produced on the reaction in terms of the masses, the angles and

*p*.

_{1}## 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.