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Mathematics, 14.02.2020 05:46 OojohnnyoO116
A bucket is being lifted from the bottom of a 50-foot deep well; its weight (including the water), B, in pounds at a height h feet above the water is given by the function B(h). When the bucket leaves the water, the bucket and water together weigh B(0)=20 pounds, and when the bucket reaches the top of the well, B(50)=12 pounds. Assume that the bucket loses water at a constant rate (as a function of height, h) throughout its journey from the bottom to the top of the well. a. Find a formula for B(h). b. Compute the value of the product B(5). Δh, where Δh=2 feet. Include units on your answer. Explain why this product represents the approximate work it took to move the bucket of water from h=5 to h=7. c. Is the value in (b) an over- or under-estimate of the actual amount of work it took to move the bucket from h=5 to h=7? Why? d. Compute the value of the product B(22).Δh, where Δh =0.25 feet. Include units on your answer. What is the meaning of the value you found? e. More generally, what does the quantity Wslice= B(h)Δh measure for a given value of h and a small positive value of Δh? f. Evaluate the definite integral ∫ B(h) dh. What is the meaning of the value you find? Why?
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A bucket is being lifted from the bottom of a 50-foot deep well; its weight (including the water), B...
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