# Math

A bucket that weighs 3.2 pounds and a rope of negligible weight are used to draw water from a well that is 82 feet deep. The bucket is filled with 42 pounds of water and is pulled up at a rate of 2.3 feet per second, but water leaks out of a hole in the bucket at a rate of 0.35 pounds per second. Find the work done pulling the bucket to the top of the well.

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1. The net mass of the bucket as a function of time, M(t)
=3.2+42-0.35t
Work done as a function of time
= M(t)*2.3 ft/s * 32.2 ft/s^2
Over the height of the well,
time required to go to the top
= 82'/2.3 '/s
= 82/2.3 s
Total work done
= ∫ M(t)*32.2 * 2.3dt from 0 to 82/2.3
=[45.2t-0.175t²] from 0 to 82/2.3
= 102872 poundal-ft
= 3194.8 lbf-ft (after dividing by g)

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2. what's the 32.2ft/s^2

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3. Acceleration due to gravity

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