a) A skier traveling at 28 m/s encounters a 24 degree slope. If you could ignore

Question

a) A skier traveling at 28 m/s encounters a 24 degree slope. If you could ignore friction, to the nearest meter, how far up the hill does he go?

b) If the coefficient of kinetic friction in the previous problem was actually .15 and the slope 30 degrees, to the nearest meter how far up the hill does he go?

I draw the force-body diagram for this problem but I can't quite figure out where to go after I draw the diagram... I missed both review days because I was sick so any help is greatly appreciated for the test is tomorrow.

Explanation / Answer

conserving energy,
all the K.E wiil be converted to P.E
so, .5*m*28^2 = m*9.8*l*sin24   (height it travels = l*sin24 where l=distance covered up on the hill)
so, l = 98.34 m = 98m <----answer(a)

b)conserving energy similarly,
all the K.E will be converted to P.E and work done by friction, so,
.5*m*28^2 = m*9.8*l*sin30 + .15*m*9.8*cos30*l (as frictional force = mg*cos30 and the distance travelled = l   so, work done = mg*cos30*l)
so, l = 63.5 m = 64m ,----answer(b)

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