Abucket that weighs 5 lb and a rope of negligible weight are used to draw water from a well that is 80 ft deep. the bucket is filled with 42 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. (let x be the height in feet above the bottom of the well. enter xi* as xi.)

We can conclude that the work applied is 3440ft-lb

Explanation:

Water leaks out of te bucket at rate of

We define now that the Force here is just the water x feet above the bottom and the combined weight of the bucket.

In an equation we can arrange that,

The integral of a Force is the Work.

We can conclude that the work applied is 3440ft-lb.

kepler used the data from tycho blahe (his mentor) to construct the laws of planetary motion.

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