Conservation of energy related question

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Homework Statement


A skier of mass m starts from test at the top of a solid sphere of radius r and slides down its frictionless surface. (a) At what angle [tex]\theta[/tex] will the skier leave the sphere? (b) If friction were present, would the skier fly off at a greater or lesser angle?
http://img158.imageshack.us/img158/2091/chp8pro24pu5.png [Broken]

Homework Equations


Conservation of energy (because this problem is from that chapter)

The Attempt at a Solution


The skier will leave the sphere if the normal force becomes zero. So radially:
[tex]mg \cos \theta - N = \frac{mv^2}{r}[/tex]
[tex]mg \cos \theta = \frac{mv^2}{r}[/tex]
[tex]v^2 = rg \cos \theta [/tex]
Then, taking the potential energy reference to be the height when the skier leaves the sphere,
[tex]E_i = E_f[/tex]
[tex]K_i + U_i = K_f + U_f[/tex]
[tex]0 + mg(r - r \cos \theta) = 1/2 m (rg \cos \theta) + 0[/tex]
But this doesn't work if I try to solve for theta!
 
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