Physics problem: connected inclined planes

Question

There are two inclined planes with the same curvature and the same mass M put on a horizontal surface. A small body of mass m is set to slide off (without friction) from height h on one plane. Find:

a) what is the maximum height the body m will reach after sliding off the first plane, then going up the second one.

b) what will be the velocities of the three objects the moment when the body m reaches the maximum height.

Answer 1

Sorry, my last answer had an error in it and I considered the slopes unconnected. Let's try again... We can do an energy and a horizontal momentum balance for the whole system and the entire process.

energy balance mgh = 1/2 (m+2M)v_M² + mgh' (The mass at the end is still with respect to the slope, so it has kinetic energy 1/2 mv_M² where v_M is the velocity of the large masses.

horizontal momentum: 0 = (2M+m)v_M , so v_M = 0 which implies h'=h.

The unconnected problem is a lot more complicated and interesting. This analysis is akin to the result of trying to move something internally with internal forces. I apologize if I missed something here.