Calculating Work Done by Kinetic Frictional Force on a Coasting Skier

[workhard]

A 67.9kg skier coasts up a snow-covered hill that makes an angle of 27.7o with the horizontal. The initial speed of the skier is 8.54m/s. After coasting a distance of 1.94m up the slope, the speed of the skier is 3.15m/s. Calculate the work done by the kinetic frictional force that acts on the skis.

This is a problem that I seem to keep getting wrong. I have spent over an hour on it now...

so far I have come up with that i will find my initial and final KE by .5mv^2

How do I incorporate the conservational equation into this?

My mind is jumbled

Thanks.

 

[Chi Meson]

change in KE = (-) change in PE + Q. (Q is heat generated through work done by friction)