Question

A skier starts at rest on the top of Mt Circular, a strange, smooth, icy hill shaped like a hemisphere. The hill has a constant radius of R. Neglecting friction (it is icy!), show that the skier will leave the surface of the hill and become air-borne at a vertical distance of h=R/3, measured from the top of the hill.

I think the way to do it is to use forces, since at R/3 Fn=0, and combine that with conservation of energy, but everything I try just leads in one big circle and I can't get anywhere.

Answer 1

The normal component of weight has to less than centripetal force. Solve that .