Answer to Question #86980 in Mechanics | Relativity for Maria

Question

A 65-kg skier grips a moving rope that is powered by an engine and is pulled at constant speed to the top of a 23∘ hill. The skier is pulled a distance x = 330 m along the incline and it takes 2.0 min to reach the top of the hill.
If the coefficient of kinetic friction between the snow and skis is μk = 0.10, what horsepower engine is required if 30 such skiers (max) are on the rope at one time?
Express your answer using two significant figures.

Answer 1

$$Pt=N(mgh+\mu_k mgx)$$

$$P=\frac{Nmgx(\sin(23)+\mu_k)}{t}$$

$$P=\frac{30(65)(9.8)(330)(\sin(23)+0.1)}{120}=25789 W$$

Or 35 hp.