An out-of-control truck with a mass of 5000 kg is traveling at 35.0 m/s when it

Question

An out-of-control truck with a mass of 5000 kg is traveling at 35.0 m/s when it starts descending a steep (15 degree) incline. The incline is icy, so the coefficient of friction is only 0.30. Use the work-energy theorem to determine how far the truck will skid (assuming it locks its brakes and skids the whole way) before coming to rest. I don't understand the last part with Fd=K-Ki. I can't follow the variables. Which is f, k, and ki? I understand that you solve for d. And why use Fd instead of W?
Also, in the diagram, I don't understand mgcos? and mgsin?. Why are they labeled like that and in that position? Thanks.

Explanation / Answer

In last part    From work energy theorem                       Work done = Change in kinetic energy From definition                   work done = Force * displacement                               W = F * d                                               where F = Force applied on the truck                                                          d = distance travelled by the truck So we use Fd instead of W,both are same. ----------------------------------------------------------------------------------------------------------------- In                  Fd = K - K0    part                                         Fd = W = Work done on the truck                                          K0 = Initial Kinetic energy before comes to rest                                           K = Final kinetic energy after coming to rest = 0 Here K = ZERO because after coming to rest the truck has no velocity, so          K = (1/2)m(0)^2 = 0. and K0 = (1/2)m(v0)^2 , because intially it moves with velocity v0 . ----------------------------------------------------------------------------------------------------------------- In the diagram the Weight of the body mg is clearly a vector,which always acts vertically downward direction. Every vector resolves in to two components which are perpendicular to each other. Here 'mg' resolved in to two perpendicular components mg cos? and mg sin? .

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