Question: Assume the bucket in Example 4 is leaking. It starts with 2 gallons of

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Question: Assume the bucket in Example 4 is leaking. It starts with 2 gallons of water (16 lb) and leaks at a constant rate. It finishes draining just as it reaches the top. How much work was spent lifting the water alone? (Hint: do not include the rope and bucket, and find the proportion of water left at elevation x ft.)

"Example 4": A (**not included because someone before used it and wasn't supposed to, this is for reference**)-lb bucket is lifted from the ground into the air by pulling in 20 ft of rope at a constant speed. the rope weighs (**not included**) lb/ft. I need the answer from the first paragraph.

The question is an extension from an example in our book, but the book doesn't give the answer.

Thanks for the help, and sorry for the confusion. Please show work.

Explanation / Answer

rate of water leaking=a let the speed be v
mass of water left=2-ax/v
work done in lifting it=(2-ax/v)gxdx,integrating it from 0 to 20

=g(x^2-ax^3/(3v))

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