Sliding Stick against a Wall

Homework Statement

A planck of length L2 leans against a wall. It starts to slip downwards without friction. Show that the top of the plank loses contact with the wall at 2/3 of it's original height.

Homework Equations

F*R = torque
Moment of Inertia of Rod (I) = 1/3 M4L$$^{2}$$
Mgh = $$\frac{1}{2}$$MV$$^{2}$$ + $$\frac{1}{2}$$I$$\omega$$$$^{2}$$

The Attempt at a Solution

I've been trying this problem for over two hours now and can't seem to get it to work. My initial idea was to work with torques, but I didn't seem to be getting anywhere so I tried the Mgh formula above, setting h as the height of the center of mass (1/2h) and trying to solve for h knowing that at the point the rod leaves the wall the horizontal velocity should be equal to the horizontal component of the radial velocity. So far I can't seem to get the equations to work out, any help would be very much appreciated.

The problem also has a hint:
Only a single variable is needed to describe the system. Note the motion of the center of mass.