A bucket with a mass of one kilogram and a rope of negligible weight are used to draw water from a well that is 10 meters deep. The bucket is filled with 20 liters of water, and is pulled up at a rate of 0.5 meters per second. As the bucket is pulled up, water leaks out at a rate of 0.1 liters per second. (a) How long does it take to pull the bucket to the top of the well?
(b) What is the mass of the bucket (plus water) when it has been raised у meters?
(c) What is the weight force of the bucket (plus water) when it has been raised у meters? Hint: the density of water is one kilogram per liter
(d) Write an integral for the work done to raise the bucket to the top of the well.
(e) Evaluate the integral in part (d).