Here is the question I need help on:

A hemispherical pile of snow with a height of 20 m is piled up. An extreme skier starts at the top of this snowball, and she skies down finding that everytime she tries it she flies off at the same angle α with respect to a vertical line from the center of the hemisphere of snow to the top. Neglecting friction between skies and snow, estimate this angle. How would the angle change if you include friction?

By my understanding, the velocity is perpendicular to the "string" tension which pulls it towards the center. However, the skier isn't really "tied" to the center here so I'm not sure at what point you'd say the skier breaks from the hemisphere and goes off at the angle. I'm assuming it is 90 degrees at to the radius at the point of breaking but without knowing when the skier flies off, I'm not sure how to find the angle with respect to the vertical line. Any help? Hopefully I'm not on the wrong path completely.