Consider a system of a cliff diver and the earth. The gravitational potential energy of the system decreases by 24,500 J as the diver drops to the water from a height of 44.0 m. Determine her weight in newtons.

Before she jumped from the cliff, her gravitational potential energy was

GPE = (her weight) x (height of the cliff) .

That's exactly the GPE that she lost on the way down to the water.  So we can write

24,500 J = (her weight) x (44.0 m)

Divide each side by 44.0 m:

Her weight = 24,500 J / 44 m

Her weight = 556.8 Newtons

(about 125 pounds)

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