This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Math 182 Homework Section 6.5 Problem 12 A bucket that weighs 4lbs and a rope of negligible weight are used to draw water from a well that is 80 feet deep. The bucket is filled with 40lbs of water and is pulled up at a rate of 2 feet second . However, water leaks out of a hole in the bucket at a rate of . 2 lbs second . Find the work done in pulling the bucket to the top of the well. t seconds after the process begins we have that the height of the bucket is y = 2 t on the scale shown in the diagram. The weight of the bucket and water at this time is 4lbs and 40 . 2 t lbs respectively. Therefore, as a function of height y , the total weight of the bucket and water is (we replace t by y 2 ) to get 4 + 40 . 2 y 2 = 44 y 10 . The work required to move this bucket a tiny distance dy is thus (44 . 1 y ) dy . Therefore, the total work to raise the bucket is integraldisplay 80 (44 . 1 y ) dy = bracketleftbig 44 y . 05 y 2 bracketrightbigvextendsingle vextendsingle y =80 y =0 = ( 44 80 . 05 (80) 2 ) 0 = 3200 ftlbs...
View
Full
Document
 Spring '08
 Keppelmann
 Math

Click to edit the document details