Solve m2 & v2' Elastic Collision: Ball A & B Velocity/Mass

[erikewell]

"Ball A with mass 4kg is moving with a velocity of 8m/s North when it crashes into Ball B with unknown mass moving with a velocity of 6 m/s West. This collision is perfectly elastic. If Ball A ends up moving with a velocity of 6.5 m/s @ 120 degrees after the collision, find the final mass and final speed of Ball B if it moves at an angle of 160 degrees after the collision."

The formula to calculate an elastic collision is m1v1 + m2v2 = m1v1' + m2v2', where v1' and v2' represent velocities after the collision, m1 and 2 meaning masses and v1 and 2 meaning velocity before collision.

I know what I have to do, but I have no idea how to rearrange the equation to solve for both m2 and v2'. Could you guys help me with solving this? I'd really appreciate it.

 

[Kilgour22]

"Ball A with mass 4kg is moving with a velocity of 8m/s North when it crashes into Ball B with unknown mass moving with a velocity of 6 m/s West. This collision is perfectly elastic. If Ball A ends up moving with a velocity of 6.5 m/s @ 120 degrees after the collision, find the final mass and final speed of Ball B if it moves at an angle of 160 degrees after the collision."

The formula to calculate an elastic collision is m1v1 + m2v2 = m1v1' + m2v2', where v1' and v2' represent velocities after the collision, m1 and 2 meaning masses and v1 and 2 meaning velocity before collision.

I know what I have to do, but I have no idea how to rearrange the equation to solve for both m2 and v2'. Could you guys help me with solving this? I'd really appreciate it.

What does it mean for a collision to be "perfectly elastic"? Perhaps this tells us something about one of the variables, so we can solve for the other unknown?

Also, what does conservation of momentum tell us?

 

[Kilgour22]

To expand a little bit and perhaps shed some more light about what I'm getting at, remember that momentum is a vector quantity and can therefore be broken into x and y parts. Conservation of momentum tells us something very important relating to this that we can use to solve these types of problems.