How Do You Solve an Off-Center Elastic Collision Problem?

[jromeo]

Homework Statement

Homework Statement
The mass m1 has the velocity (v1i)\hat{i} and makes an off-center collision with m2=2m1. The final velocities are v1f=a1\hat{i}+b1\hat{j}, and v2f=a2\hat{i}+b2\hat{j}. Assuming elastic collision and v2i=0m/s, obtain the values of a1, a2, and b2 for the given value of b1. Also obtain the angles \theta1 and \theta2 of v1f and v2f with the x-axis. Retain the solutions for a1>0.

m₁ = 3.20kg
v_1i = 11.2m/s
b₁ = 4.12m/s

Homework Equations

The Attempt at a Solution

First I broke down the conservation of momentum equation into it's vector components.
m₁v_1i = m₁a₁ + m₂a₂ and 0 = m₁b₁ + m₂b₂. I then solved for b2 by setting b2 equal to
-m₁b₁/m₂. Then I attempted to solve for a₁ and a₂ by using KEi=KEf because energy is conserved in elastic collisions. KEf = 1/2m₁v_1i² = 1/2m₁(a₁² + b₁²) + 1/2m₂(a₂² + b₂²)

I keep getting the wrong units when I solve for a₁ or a₂ in one equation though. I can't figure out what I'm missing about this problem. Thanks in advance for any help!

 

[djeitnstine]

Ok your first step is correct however to simplify matters, you can use V1 - V2 = -(V1 - V2) (x and y components of course)

Then solve for either V1 or V2 and plug it into your momentum equations.

Also note that the final angle adds up to 90 degrees