Resulting directions and velocities of two circles colliding

[yortzec]

Homework Statement

I am trying to find the resulting x and y velocities when two moving circles (particles) which are exactly the same in mass and size and are in the same plane, collide, given the x and y velocities and coordinates of the two particles.

What is the formula for the resulting x and y velocities given the original x and y velocities and the coordinates of the circles at the exact point when the circles meet?

Homework Equations

The following formulas show the math for two particles using vectors and given the mass, but I don't know the mass off the particles, just that they are the same. Also, I am confused on how to convert vectors in a general formula to x- and y-velocities.

The kinetic energy is below, I don't know if this helps:

The Attempt at a Solution

Using the above formulas, and assigning a generic mass of 1g, I obtained two vectors which seemed to work. But how can I convert this to x- and y-coordinates in a formula?

Thanks for helping!

 

[Spinnor]

This has been solved many times. If you just need the answer start here,

http://en.wikipedia.org/wiki/Elastic_collision#Two-_and_three-dimensional

Found via,

https://www.google.com/webhp?hl=en#...w.,cf.osb&fp=243aec9c1865a62f&biw=734&bih=439

 

[yortzec]

Thanks, Spinnor. I see that if we add, say, the original x-velocities together, we get the sum x-velocity of both of the circles. However, the circles do not move the same direction after they collide. I am having trouble deriving the addends (the final x-velocities for each). For example, can find SOME NUMBER in this:

x₁ + x₂ = SOME NUMBER.

But how do I find x₁ given this?