What Distance Must a Rock Fall to Double Its Speed?

[swede5670]

Homework Statement

After falling 5m a rock has a velocity of v. What is the total distance the rock must fall to get a speed of 2v?

Homework Equations

GPE=mgh
Ke=1/2mv^2

The Attempt at a Solution

Should I set both equations equal to each other? I'm not even sure how to begin this one.

 

[LowlyPion]

You can do it that way. Note that v = (2*g*h)^½

If v ∝ h^½ ...

... how much then do you need to increase the height to get a doubling of speed?