Calculating Work Done by Kinetic Frictional Force on a Coasting Skier

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To calculate the work done by the kinetic frictional force on a skier coasting up a hill, first determine the initial and final kinetic energy using the formula 0.5mv^2. The change in kinetic energy (KE) can be calculated by subtracting the final KE from the initial KE. Incorporate the conservation of energy equation, which states that the change in KE equals the negative change in potential energy (PE) plus the heat generated (Q) from friction. By rearranging the equation, the work done by friction can be isolated and calculated. This approach will clarify the relationship between kinetic energy, potential energy, and the work done by friction.
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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.
 
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change in KE = (-) change in PE + Q. (Q is heat generated through work done by friction)
 
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