Skier on a sphere problem involving conservation of energy

[BJducky]

Homework Statement

A skier of mass m starts from rest at the top of a solid sphere of radius r and slides down its frictionless surface. At what angle (theta) will the skier leave the sphere? And if friction were present, would the skier fly off at a greater or lesser angle?

Homework Equations

I am assuming that we will use the conservation of energy, perhaps mgh=1/2mv^2. Something like that?

The Attempt at a Solution

Honestly, I am completely at a loss. I tried to approach this problem with some of the formulas in the book but could not figure it out. Please help me.

 

[Hootenanny]

Rather than considering conservation of energy, a better approach may be to examine the forces acting on the skier, paying particular attention to the normal reaction force.