How to Solve 2D Collision Billiard Balls

[Hotsuma]

Homework Statement

Two billiard balls of equal mass move at right angles and meet at the origin of an xy coordinate system. Initially ball A is moving upward along the y-axis at 2.0, and ball B is moving to the right along the x-axis with speed 3.7$m/s$. After the collision (assumed elastic), the second ball is moving along the positive y axis.

Image:

http://session.masteringphysics.com/problemAsset/1057762/8/GIANCOLI.ch09.p056.jpg

Homework Equations

x direction: m_b*v_b = m_a*v_a*cos(\theta)
y direction: m_a*v_a = m_a*v'_a*cos(\theta) + m_b*v'_b*sin(\theta)

The Attempt at a Solution

I have tried plugging in the given values into those equations, but then i cannot solve for anything because I have too many unknowns. I have tried to solve for v'_a first but without any luck. I also tried combining the equations to no luck.

Please help!

 

[Nabeshin]

You should start from the basic principles and work your way to the specific solution rather than just plugging into an equation!

Think about which quantities will be conserved in this scenario and write down the corresponding conservation equations. Then see if you can solve for one of the variables.

 

[Hotsuma]

Oh, I totally figured it out already, thanks. I actually didn't add the potential energy of the spring. i figured it out already, thanks.