Diabolical Engine II

A physics student irritated by the personal mannerisms of their physics professor decides to rid the world of him. The student plans to drop a large, massive object (the statue of Washington Duke, actually, recently stolen by pranksters from his fraternity), mounted on nearly frictionless casters, from a tall building of height $H$ with a smooth roof sloped at the angle $\theta$ as shown. However, the student (being a thoughtful sociopath) wants to make sure that the mass $M$ will make it over the roses to the path a distance $D$ from the base of the building and needs to know how far to let the statue roll down the roof to get the right speed.

Unfortunately, the student isn't very good at physics and comes to you for help. Since they don't want to tell you which building or which path they want to use (you might be able to testify against them!) they want you to find (in two steps, each counting as a separate problem) a general formula for the requisite distance.

a) Help them out. Start by finding $v_0$ in terms of $H$, $M$, $D$, $\theta$ and $g$ (the gravitational constant) that will drop $M$ on RGB assuming no friction or drag forces. (That way I'm still pretty safe). (20 points.)

b) Now that you know the speed (or rather, assuming that you know the speed, as the case may be) find $h$ (the vertical distance the statue must roll down, released from rest, to come off with the right speed). Explicitly show that your overall answer (in which $v_0$ should NOT appear) has the right units. If you were clueless in problem 4) you may leave $v_0$ in your answer but should still try to find SOME combination of the letters $H$, $M$, $D$, $\theta$ and $g$ that has the right units and varies the way you expect the answer to (more height $H$ means smaller $h$, for example, so it probably belongs on the bottom). (20 points.)