Answer :
The work done in hauling the bucket to the top of the well is 16ft/lb.
Using Riemann sum to calculate the area underneath a graph or curve.
At a rate of 0.15 lb/s, water escapes from a hole in the bucket. Convert this rate to inches per foot.
Q = 0.15 ÷ 1.5
Q = 0.01
As an outcome, water escapes at a rate of 0.01 lb/ft via a hole in the bucket.
Let x be the height in feet above the well's bottom. Thus, the total amount of water that leaks out of the hole is 0.01x The bucket is originally filled with 44 lb of water, and then 0.01x water seeps out. As a result, the water left in the bucket is,
44 - 0.01x
The bucket weighs 5 pounds. As a result, the total weight of the bucket when it reaches the top of the well is,
(44 - 0.01x) + 5
Because the well is 60 feet deep. As a result, the integration should be limited to a range of 0 to 60 feet. Take the above x function and solve it using the Riemann sum method.
W = [tex]\int\limits^{60}_{0} {44 - 0.01x + 5} \, dx[/tex]
W = | 0 - 0.01 (x² ÷ 2) + 0|[tex]{{}_{0}^{60}}[/tex]
W = 0.005(60)² - 0
W = 16 ft/lb
Read more about the Riemann sum method at
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