Instantaenous velocity/center of mass? help

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The discussion revolves around a physics problem involving a 10 kg wedge on a frictionless surface and a 5 kg block sliding down its inclined surface. The block has a vertical velocity of 3.0 m/s and a horizontal velocity of 6.0 m/s at a specific moment. Participants express uncertainty about how to approach the problem, particularly regarding the center of mass and the mechanics of the wedge's movement due to the block. Key questions include the equations of motion for the center of mass and the relationship between the block's motion and the wedge's response. Clarifying these concepts is essential for solving the problem effectively.
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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?
 
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