Physics Phrustration...?

Question

A 67.9kg skier coasts up a snow-covered hill that makes an angle of 27o with the horizontal. The initial speed of the skier is 8.0m/s. After coasting a distance of 2.0m up the slope, the speed of the skier is 3.00m/s. Calculate the work done by the kinetic frictional force that acts on the skis.

This is my last problem of my 20 that I needed to do. I have created a sketch to try and figure out other variables, but nothing seems to be coming together. I found out the PE and KE, but am unsure how it can be used with the negative acceleration that I also found. It seems like I am making it harder then it really is. Should I use sin to find out the height cahnge?

my equation comes out to...

used change PE = mg(hf - hi)
to get 600.07

336.87 - 2476.03 = 600.07 + frictional force

I get -2739 as an answer, but it is still wrong.

Answer 1

You are on the right track. Two things remove energy from the skier: frictional force and change in potential energy due to elevation change. The elevation change as you said is ∆h = S*sin(T) where T is the angle of the slope. The energy change from this is m*g*∆h. His starting energy is .5*m*v0^2 where v0 is the starting velocity. The ending energy is .5*m*Vf^2.

The relation is:

end energy - start energy = ∆potential energy + friction energy.

You have all the information needed to solve this relation. Don't worry about negative acceleration--as you can see, you don't have to figure it. Even if you did, there is nothing odd about negative acceleration--it just means the object is slowing down, not speeding up.