Homework Help: Block and wedge. Analysis of the center of mass

1. May 20, 2007

clicwar

1. The problem statement, all variables and given/known data
A block of mass m rests on a wedge of mass M and height H which, in turn, rests on a horizontal table. All the surfaces are frictionless.
If the system starts at rest with the block on the top of the wedge, find the displacement of the wedge during the time the block descends to the bottom.
Consider "alpha" as the inclination angle of the wedge related to the horizontal surface.

2. Relevant equations
Center of Mass equations and concepts

3. The attempt at a solution
Using pseudoforces i have first encountered the accelerations of the block and wedge, then the time taken by he block to slide down the wedge and then applying the kinematics equations to the wedge i encountered the displacement , which is D = H m cot("alpha")/(M+m)

BUT i'm sure that there is a easier method to solve this problem using the concept of center of mass(since there is no horizontal external force acting on the system the horizontal component of the center of mass position should be at rest, right?), but i'm stuck.
Could someone help me(or teach me) to find a easier way to get the answer without have to calculate all the accelerations as i have made in the long solution above.