I'm struggling with this problem:
From George Simmons_ Differential Equations
At sunset a man is standing at the base of a dome-shaped hill where if faces the setting sun. He throws a rock straight up in such a manner that the highest point it reaches is level with the top of the hill. As the rock rises, its shadow moves up the surface of the hill at a constant speed. Show that the profile of the hill is a cycloid.
I've tried different things and I showed that the $x$ component and the $y$ component of the shadow should move with constant speed, but nothing really other than that.