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A skier is pulled by a tow rope up a frictionless ski slope that makes an angle of 16° with the horizontal. The rope moves parallel to the slope with a constant speed of 1.0 m/s. The force of the rope does 690 J of work on the skier as the skier moves a distance of 9.0 m up the incline. (a) If the rope moved with a constant speed of 2.5 m/s, how much work would the force of the rope do on the skier as the skier moved a distance of 9.0 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 m/s and (c) 2.5 m/s?

Question

A skier is pulled by a tow rope up a frictionless ski slope that makes an angle of 16° with the horizontal. The rope moves parallel to the slope with a constant speed of 1.0 m/s. The force of the rope does 690 J of work on the skier as the skier moves a distance of 9.0 m up the incline. (a) If the rope moved with a constant speed of 2.5 m/s, how much work would the force of the rope do on the skier as the skier moved a distance of 9.0 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 m/s and (c) 2.5 m/s?

check_circleAnswer
Step 1

(a). The rope is moving with constant speed, so the change in kinetic energy is zero.

Hence, the work done by the force of the rope on the skier is

W 690 J
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W 690 J

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Step 2

(b). The rate of work at v=1m/s, th...

dW
Power
dt
690J
9s
=76.66 W
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dW Power dt 690J 9s =76.66 W

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