$6\mathrm{.}41$ This problem utilizes most of the important laws introduced so far and it is worth a substantial effort. However, the problem is tricky $($although not really complicated$),$ so don't be alarmed if the solution eludes you.

A plank of length $\backslash (2$ L $\backslash )$ leans against a wall. It starts to slip downward without friction. Show that the top of the plank loses contact with the wall when it is at two$-$thirds of its initial height.

Hint: Only a single variable is needed to describe the system. Note the motion of the center of mass.