Question

You raise a bucket of water from the bottom of a deep well. If your power output is 101 W, and the mass of the bucket and the water in it is 6.00 kg, with what speed can you raise the bucket? Ignore the weight of the rope.

Answer 1

W=ΔK+ΔU


where K is the kinetic energy and U is the potential energy
Work is a change in the kinetic energy or a change in the potential energy.
In th problem which energy is changing?? Keep in mind that they have asked what speed at which you can pull it up... which would be constant.

P = W/t
the work done is a change in the potential energy ONLY.
so W=mgΔh

where h = vertical displacement