A rope is strung between two trees, see the figure on the left.  The trees are 100 feet apart, and the rope is attached 100 feet above the ground on one tree and 50 feet above the ground on the other.  The rope is 120 feet long.

A small wheel is attached to the rope allowing you, by holding on to the wheel, to roll from one end of the rope to the other.  As you hang from the rope, it becomes taut.

What is the path, both algebraically and geometrically, described by the wheel as you roll from one tree to the other?  At what point is the path closest to the ground? 

For the more adventurous: Solve the same problem in general, with the trees being A feet apart, the rope attached at height T feet on the tall tree and B feet on the shorter tree.