# Momentum and Collisions in 2 dimensions

1. Jan 14, 2009

### cheese825

1. The problem statement, all variables and given/known data
Two particles with masses 2m and 3m are moving toward each other along the x axis with the same initial speeds v. Particle 2m is traveling to the left, while particle 3m is traveling to the right. They undergo an elastic, glancing collision such that particle 2m is moving downward after the collision at a right angle from its initial direction.

2. Relevant equations
v2 = final velocity of the 3m object
v3 = final velocity of the 2m object
angle w = the angle of 3m to the horizontal after colliding with the 2m

momentum conserved in x-dimension:
3mv - 2mv = 3m * cos(w) * v2

momentum conversed in y-dimension:
0 = (3m * sin(w) * v2) - (2m * v3)

kinetic energy is also conserved:
.5(3m)(v^2) + .5(2m)(v^2) = .5(3m)(v2^2) + .5(2m)(v3^2)

3. The attempt at a solution
pages of work of which i am too tired now to transcribe into type

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2. Jan 14, 2009

### Carid

You have three equations and three unknowns.
How about start by simplifying the equations and doing some substitutions.
Then maybe you can use.
sin²w + cos²w = 1
It's long winded but it works....
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