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A bucket that weighs 3 lb and a rope of negligible weight are used to draw water from a

well that's 60 feet deep. Suppose the bucket starts with 37 lb of water and is pulled up by a rope at 2 ft/sec, while water leaks out of the bucket at a rate of 1/4 lb/sec.

A. How long does it take for the bucket to get to the top of the well? Write an equation that

expresses the total weight of the bucket as a function of time, as the time varies from 0 until the time the buckets gets to the top.

B. Recall that work equals force times distance. Calculate the work done in lifting the bucket

to the top of the well, keeping in mind that here force is equal to weight.

For A:I did 60ft/2ft/s=30 sec so it takes 30 secs for the bucket ot get to top of well

equation: Weight=40+ integral sign from 0 to 30 (-1/4)dx =32.5 lb

For B: i did total work= integral sign from 0 to 60 (32.5x)dx

i don't know if I am doing this right. I've searched the internet and found a question similar to mine (question #6):

http://count.ucsc.edu/~bauerle/images/19BW07HWK/Homework 6.4 Math 19B Winter 2007, Bauerle.pdf"

and I've used the same steps that i did for this question but i got the wrong answer.

well that's 60 feet deep. Suppose the bucket starts with 37 lb of water and is pulled up by a rope at 2 ft/sec, while water leaks out of the bucket at a rate of 1/4 lb/sec.

A. How long does it take for the bucket to get to the top of the well? Write an equation that

expresses the total weight of the bucket as a function of time, as the time varies from 0 until the time the buckets gets to the top.

B. Recall that work equals force times distance. Calculate the work done in lifting the bucket

to the top of the well, keeping in mind that here force is equal to weight.

For A:I did 60ft/2ft/s=30 sec so it takes 30 secs for the bucket ot get to top of well

equation: Weight=40+ integral sign from 0 to 30 (-1/4)dx =32.5 lb

For B: i did total work= integral sign from 0 to 60 (32.5x)dx

i don't know if I am doing this right. I've searched the internet and found a question similar to mine (question #6):

http://count.ucsc.edu/~bauerle/images/19BW07HWK/Homework 6.4 Math 19B Winter 2007, Bauerle.pdf"

and I've used the same steps that i did for this question but i got the wrong answer.

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