At what angle does a skier lose contact with a frictionless snowball?

[eil2001]

Ok, here's the question:

A skier starts at the top of a very large frictionless spherical snowball, with a very small initial velocity, and skis straight down the side. At what point does she lose contact with the snowball and fly off at a tangent? That is, at the instant when she loses contact with the snowball, what angle does a radial line from the center of the snowball to the skier make with the vertical?

So, I want to use K_1 + U_1 = K_2 + U_2, but I am confused b/c there are no numbers. The answer is 48.2 degrees, but I don't see how they get this.

Thanks for any help!

 

[pmrazavi]

when she is about to lose contact, the Normal force is zero. At the top of the cliff the only type of energy is Pot. grav. (mgh), but when she is about to lose contact she has both potential and kinetic energy which their sum is equal to the first mgh.
You should find the angle by computing the second height.

 

[eil2001]

At the top of the snowball, isn't there kinetic energy, too, b/c the problem says that the skier starts with a small initial velocity? Or, is that "small" supposed to mean negligible? Also, how do I find the height at which the skier leaves the snowball? I feel like it's something w/angles and sines/cosines, but I'm not sure. Thanks!