Question

A ski lift carries a 75.0-kg skier at 3.00 m/s for 1.50 min along a cable that is inclined at an angle of 40.0° above the horizontal. a. How much work is done by the ski lift? b. How much power is expended by the ski lift?

Answer 1

Answer

given,

mass of the ski = 75 Kg

speed of the skier, v = 3 m/s

time = 1.50 min = 90 s

angle of inclination, θ = 40°

distance = s x t

              = 3 x 90 = 270 m

a) W = F. d cos θ

   W = mg. d cos θ

   W = 75 x 9.8 x 270 x cos 40°

    W = 152021.52 J

work is done by the ski lift is equal to  152021.52 J

b) Power extended by the ski

 $Power = \dfrac{Work\ done}{time}$

$Power = \dfrac{152021.52}{90}$

      P = 1689.13 Watt.

power is expended by the ski lift is equal to 1689.13 W.