A bucket is being lifted from the bottom of a 50-foot deep well; its weight (including the water),

** (a) ** Find a formula for

** (b) ** Compute the value of the product

What are the units on the product

** (c) ** Is the value in (b) an over- or under-estimate of the actual amount of work it took to move the bucket from

Answer:

** (d) ** Compute the value of the product

What are the units on the product

** (e) ** Notice that the value in part (d) estimates the amount of work it takes to move the bucket from a height of 22 feet to 22.25 feet. More generally, the quantity

** (f) ** Evaluate the definite integral

What is the meaning of the value you find? Why?

You can earn partial credit on this problem.