What Is the Velocity of a Leaking Bucket at the Moment It Empties?

[north_pole]

Homework Statement

A bucket of mass M (when empty) initial at rest and containing a mass of water is being pulled up a well by a rope exerting a steady force P. The water is leaking out of the bucket at a steady rate such that the bucket is empty after a time T. Find the velocity of the bucket at the instant it becomes empty.

Homework Equations

rocket equation:
Fext = m dv/dt - Vrel dm/dt

The Attempt at a Solution

the total mass of the bucket and water is M' = M + m - mt/T , where m is the initial mass of the water.
The hint said " as the leaking water has zero velocity relative to the bucket.."

I don't understand it. Why Water should have zero velocity relative to the bucket?? Water is leaking out at a steady rate, so there should be a non-zero constant velocity. i am so confused.

 

[athrun200]

It is just like a aircraft drop a bomb when it flies. The bomb will move with the same speed as the aircraft.

The relative velocity of water relative to the bucket is 0, however in this question,the bucket is accelerating so the zero relative velocity only last for an instant.