Energy-related problem involving skiing up a hill

[Emethyst]

Homework Statement

A 68kg skier approaches the foot of a hill with a speed of 15m/s. The surface of the hill slopes up at 40 degrees above the horizontal and has the coefficients of static and kinetic friction of 0.75 and 0.25, respectively. Use energy conservation to find the maximum height above the foot of the hill that the skier will reach.

Homework Equations

Conservation of energy, work-energy theorem

The Attempt at a Solution

I have no idea how to solve this question; since there is friction present in the system I decided to use the work-energy theorem, thus making: E_f = E_i + W, or mgh = (1/2)mv^2 + W. The problem I'm running into is trying to figure out how to calculate a value for W seeming as there are no displacement values given in the question. How would I go about getting an answer for W, or is this the wrong way to go about this question? Any help would be greatly appreciated, thanks in advance.

 

[kuruman]

Call the height that you are looking for y. The displacement along the hillside (for purposes of calculating work) is s = y / sin40^o. So if you use the work energy theorem, you will have an equation involving only one unknown, y.