Block falling on two movable equal masses reaching new height

[newcool]

Hi, my teacher gave this problem and he said that it has a very "pretty" answer.

You have two equal masses, each mass is called M that are touching each other.

There is a block with mass m on top of the first mass M. This block is a distance H above the ground. When the block is released the first mass will start moving backwards and the block will move onto the second mass M which will start moving fowards. I have to find the new distance H, that the block will go.

Thanks in advance for any help.

Attached is a diagram

 

[newcool]

Forgot to say that there is no friction and H' has to be found in terms of m,M,H and g

 

[Justin Lazear]

Use the fact that energy and momentum are conserved to find the speed of the block and the ramp when the block is on the ground. Then do the same in reverse to find the height of the block on the second ramp.

--J