Halliday, Resnick & Walker — Kinetic Energy and Work: Problem 44

A skier is pulled by a towrope up a frictionless ski slope that makes an angle of \( 12^\circ \) with the horizontal. The rope moves parallel to the slope with a constant speed of \( 1.0 \text{ m/s} \). The force of the rope does \( 900 \text{ J} \) of work on the skier as the skier moves a distance of \( 8.0 \text{ m} \) up the incline. (a) If the rope moved with a constant speed of \( 2.0 \text{ m/s} \), how much work would the force of the rope do on the skier as the skier moved a distance of \( 8.0 \text{ m} \) up the incline? At what rate is the force of the rope doing work on the skier when the rope moves with a speed of (b) \( 1.0 \text{ m/s} \) and (c) \( 2.0 \text{ m/s} \)?