# Mechanics: conservation of momentum problem

Here's the problem:

An atom of mass 2mp with an anitial velocity vo undergos an elastic collision with an atom at rest with mass 3mp. After the collision, the first atoms trajectory deviates 30 degrees from the initial. What angle does the second atom travel from the first atoms initial trajectory?

I used conservation of momentum to get

2vo = (3)^(1/2)v1' + 3 cos(θ2) v2'

and

v1' = -3 sin(θ2)v2'

I used conservation of kinetic energy to arrive at

2(vo)^2 = 2(v1')^2 + 3(v2')^2.

So there are three equations and three unknowns (θ, v1' and v2').

After 18 pages of algebra I've decided to ask for some help. Are there trig identies that would help. I am also given θ = -65.2 but only to check with my answer, and working backwards from it didn't help.

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swindhspectrum said:
I used conservation of momentum to get

2vo = (3)^(1/2)v1' + 3 cos(θ2) v2'

and

v1' = -3 sin(θ2)v2'
Try combining these using $\sin^2\theta + \cos^2\theta = 1$. Combine that result with your equation for conservation of energy to solve for v1' & v2'.

thanks, i was skeptical of that approach but it worked out after a mess of algebra and a quadratic equation to solve