1. The problem statement, all variables and given/known data This is from Fundamentals of Physics 8th ed, by Halliday and Resnick: A boy is initially seated on the top of a hemispherical ice mound of radius R = 13.8m. He begins to slide down the ice, with a negligible initial speed. Approximate the ice as being frictionless. At what height does the boy lose contact with the ice? 2. Relevant equations This is classified under Conservation of Mechanical Energy There's a picture of a semicircle and a boy sliding down the circumference of the semicircle. 3. The attempt at a solution I don't understand what conditions would make the boy go off the ice rather than stay on the ice. I thought it had to do with centripetal forces at first (cause he's going in a circle ... for a bit) but I couldn't make that idea work.