Water is to be raised from a well 36 feet deep by means of a bucket attached to a rope. When the
bucket is full of water it weighs 70 pounds, but the bucket has a leak that causes it to lose water at the
constant rate of (1)/(2) pound for each foot that the bucket is raised.
(a) How much does the bucket weigh when the bucket is
1 foot from the bottom of the well?
pounds
10 feet from the bottom of the well?
pounds
at the top of the well?
pounds
y feet from the bottom of the well?
pounds
(b) Approximately how much work is needed to lift the bucket Delta y feet when it is y feet from the bottom of the well?
(c) Set up an integral to find the total work needed to lift the bucket from the bottom of the well to the top of the well.
int
dyft-Ib
Water is to be raised from a well 36 feet deep by means of a bucket attached to a rope.When the
bucket is full of water it weighs 7o pounds, but the bucket has a leak that causes it to lose water at the
constant rate of 1/2 pound for each foot that the bucket is raised.
(a) How much does the bucket weigh when the bucket is
1 foot from the bottom of the well?
pounds
1o feet from the bottom of the well?
pounds
at the top of the well?
pounds
y feet from the bottom of the well?
pounds
(b) Approximately how much work is needed to lift the bucket y feet when it is y feet from the bottom of the well?
(c) Set up an integral to find the total work needed to lift the bucket from the bottom of the well to the top of the well
dy ft-Ib