(adsbygoogle = window.adsbygoogle || []).push({}); Elastic Collision -- Scattering

Before I ask my question, here's the problem in full,

"A proton of mass mp, with initial velocity v0 collides with a helium atom, mass 4mp, that is initially at rest. If the proton leaves the point of impact at an angle of 45 degrees with its original line of motion, find the final velocities of each particle. Assume that the collision is perfectly elastic."

I've tried writing the momentum conservation in the x and y directions (in the laboratory frame), but I end up getting two equations with two unknowns (the deflection angles). Normally I could solve this, but the x equations are given in terms of the cosines of the angles, while the y equations are given in terms of the sines of the angles. Can anyone tell me how to write down the conservation equations in a way so that I'll be able to solve for the angles?

Also, would it be a better idea to write the equations in terms of the center of mass reference frame?

Thanks for your help.

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# Homework Help: Elastic Collision - Scattering

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