A water skier, moving at a speed of 6.10 m/s, is being pulled by a tow rope that makes an angle of 37.0 ° with respect to the velocity of the boat (see the drawing). The tow rope is parallel to the water. The skier is moving in the same direction as the boat. If the tension in the tow rope is 158 N, determine the work that it does in 13.7 s.

Question

Physics

Jackrabbit

17 April, 02:28

A water skier, moving at a speed of 6.10 m/s, is being pulled by a tow rope that makes an angle of 37.0 ° with respect to the velocity of the boat (see the drawing). The tow rope is parallel to the water. The skier is moving in the same direction as the boat. If the tension in the tow rope is 158 N, determine the work that it does in 13.7 s.

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Answers (1)

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Jarrett Freeman · Answer 1

W = 10545 J

Explanation:

The expression for the job is

W = F. D

Where blacks indicate vectors, the magnitude of this expression is

W = F D cos θ

Where the angle is between force and displacement

We have to find the displacement in the given time. The angle is between the perpendicular of the boot and the cable

x = v₀ t + ½ a t²

x = v₀ t + 0

Let's calculate the work

W = T cos 37 (v₀ t)

W = 158 6.10 13.7 cos 37

W = 10545 J