Block sliding down rough wedge on frictionless surface

[dorkymichelle]

Homework Statement

A large wedge with a mass of 10 kg rests on a horizontal frictionless surface, as shown. A block with a mass of 5.0 kg starts from rest and slides down the inclined surface of the wedge, which is rough. At one instant the vertical component of the block's velocity is of 3.0 m/s and the horizontal component is 6.0 m/s. At that instant the velocity of the wedge is:

Homework Equations

The Attempt at a Solution

I'm not really sure where to get started... I think it has something to do with the center of mass but not sure what. Also, I'm confused as to how the block can cause the wedge to move. Can someone help me get started?

 

[vela]

What is the equation of motion for the center of mass of a system? Start there.