Boy Sliding Down Frictionless Ice: Conservation of Energy

[slayer16]

Homework Statement

A boy is seated on the top of a hemispherical mound of ice. He is given a very small push and starts sliding down the ice. Show that he leaves the ice at a point whose height is 2R/3 if the ice is frictionless. (Hint:The normal force vanishes as he leaves the ice.)

Homework Equations

Conservation of energy.

The Attempt at a Solution

I wrote the normal force as function of theta. I then set the normal force equal to the centripetal force so I could get rid of the unknown velocity, but it didn't work out. I do not see any other way to solve this problem.

 

[nik21bigbang]

first you should solve for velocity by equating the normal and centripetal force then solve sin theta using the normal vanishes at the point where it leaves the surface and then put it all together in the energy conservation law mgh + (mv^2)/2= mvR then solve for h!