Question

A bucket that weighs 6 lb and a rope of negligible weight are used to draw water from a well that is 50 ft deep. The bucket is filled with 36 lb of water and is pulled up at a rate of 2.5 ft/s, but water leaks out of a hole in the bucket at a rate of 0.25 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 xp) lim Ax Express the work as an integral Evaluate the integral

Answer 1

Woxk donewrk to weright bucket t wosk to lift wate at height d x- pulling 2.5ft so total "time taken to ull wartes 5o ate el 2-5 takn to pull koter upto heigh e es u me taRn 2.5 werg coater xenaining 36-0.25 2 lo 乀,50 1o as a junchon of eimenn sum

Limon ;1 ( 36-50 vt ) 50 4.6x50 256 50(31) ニ300 50 (37) 1850 Jool