Question

A bucket that weighs 4 lb and a rope of negligible weight are used to draw water from a well that is 70 ft deep. The bucket is filled with 44 lb of water and is pulled up at a rate of 2 ft/s, but water leaks out of a hole in the bucket at a rate of 0.2 lb/s. Find the work done in pulling the bucket to the top of the well.

Show how to approximate the required work by a Riemann sum.

Answer 1

well, the weight is 44-0.2t

now integrate that over the required distance.