Power as a function of height (gravity and spring involved)

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There is a "cannon" pointing downwards with a spring inside where an object is inside and compressed up 1 meter.

mass of object = 50.0kg
k = 49050

height = 0 at bottom of cannon.

Potential energy at start = mgh + 1/2kx^2
Kinetic energy at end = 1/2mv^2

I had to first solve for the object velocity as a function of height 'y' above the bottom of the cannon.

This was: v(h) = sqrt(-981y^2 - 19.6y + 1001)

The question now is to solve for the amount of power being put out as a function of height.

We are given the answer of: p(h) = 49y * v(h), but I am to find this on my own.

I know: P = w*t, w = change in kinetic energy

The change in kinetic energy can be found pretty easily, but what do I do about time?
 

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