Two dimensional collision. Center of mass reference frames?

[yigh]

Homework Statement

[PLAIN]http://online.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?courses/phys211/oldexams/exam2/sp10/fig3.gif
A 4.0 kg circular disk slides in the x-direction on a frictionless horizontal surface with a speed of 5.0 m/s. It collides with an identical disk that is at rest before the collision. The collision is elastic. Disk 1 goes off at an angle of 60° with respect to the x-direction. Disk 2 goes off at an angle of 30° with respect to the x-direction. Treat the disks as point objects and ignore the possible rotations of the disks.

1) Why does disk two have more KE?
2) Find speed of disk 2 after collision.

Homework Equations

Conservation of momentum/Ke since the collision is elastic.

The Attempt at a Solution

My professor wants me to use center of mass reference frame (and velocity of CM) to solve this problem. I am not sure how to do this, but I do know how to calculate the Vcm before the collision. It is m1v2/(m1+m2). Vcm is same after collision so the Y velocities should cancel out. I can't quite connect that with why the KE of disk 2 is bigger, though.

 

[vela]

In the center of mass frame, the total momentum is equal to 0, so the two masses would have to have equal but opposite momenta. Initially, m1 would be moving in the +x direction and m2 would be moving in the -x direction with equal speeds. What speed would each have? What does it generally look like after the collision in the COM frame? How does that translate back to the lab frame?