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A water-skier is being pulled by a tow rope attached to a boat. As the driver pushes the throttle forward, the skier accelerates. A 73.5-kg water-skier has an initial speed of 5.2 m/s. Later, the speed increases to 12.2 m/s. Determine the work done by the net external force acting on the skier.

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Sagot :

LammettHash

Ignore my comment, that information is unnecessary.

Assuming no friction between the skis and the water, the total work performed on the skier is due only to the pulling force (T, for tension). By Newton's second law, the net force exerted on the skier is

∑ F = T = ma

where m = 73.5 kg is the mass of the skier, and a is their acceleration.

Under constant acceleration, the skier is pulled a distance x such that

(12.2 m/s)² - (5.2 m/s)² = 2ax

and solving for x gives

x = (60.9 m²/s²) / a

Then the total work performed on the skier is

W = Tx

W = ma • (60.9 m²/s²) / a

W = (73.5 kg) (60.9 m²/s²)

W ≈ 4480 J

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