Solve the all parts of given problem:

Problem: A homogeneous right wedge of mass M, horizontal length L and height H rests on a horizontal plane, with the side L on the plane. A point mass m is stuck at the top corner of the wedge. The system is initially at rest. At some point in time, the point mass starts sliding down the sloped side of the wedge, until it reaches its lower corner where it becomes stuck to the wedge. There is friction between the point mass and the wedge, but there is no friction from the horizontal plane or air resistance.

Part A: Find the final speed of the system mass-wedge.

Part B: Find the total displacement of the wedge on the horizontal plane at the end of the motion of the point particle.

I need help to compute the final speed of the system mass-wedge.