Solving the Physics of a Skier Leaving a Hill

[austindubose]

Homework Statement

A skier starts from rest at the top of a large hemispherical hill. Neglect friction and show that the skier will leave the hill becoming airborne at a distance of h=R/3 below the top of the hill. R is the radius of the hemispherical hill.

Homework Equations

Conservation of energy, balancing of forces, centripetal force = m(v²/r)

The Attempt at a Solution

I know this has to do with when the normal force becomes zero (or at least that's what I think). But I have no idea how to start this; can anyone point me in the right direction?

 

[grzz]

You are on the right track.