A Bucket Weighs $5 \mathrm { lb }$ And a Rope of Negligible Weight Are Used to Draw

Multiple Choice

A bucket weighs $5 \mathrm { lb }$ and a rope of negligible weight are used to draw water from a well that is 40 ft deep. The bucket starts with $50 \mathrm { lb }$ of water and is pulled up at a rate of $10 \mathrm { ft } / \mathrm { s }$ , but water leaks out of a hole in the bucket at a rate of $0.5 \mathrm { lb } / \mathrm { s }$ . Find the work done in pulling the bucket to the top of the well.

A) $2,160 \mathrm { ft } - \mathrm { lb }$
B) $2,660 \mathrm { ft } - \mathrm { lb }$
C) $3,660 \mathrm { ft } - \mathrm { lb }$
D) $2,260 \mathrm { ft } - \mathrm { lb }$
E) $3,160 \mathrm { ft } - \mathrm { lb }$