What Distance Must a Rock Fall to Double Its Speed?

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To determine the distance a rock must fall to double its speed, the relationship between velocity and height is crucial, as velocity is proportional to the square root of height. After falling 5 meters, the rock reaches a speed of v, and to achieve a speed of 2v, the height must be increased. The equations for gravitational potential energy and kinetic energy can be set equal to find the necessary height increase. Specifically, if v is expressed as v = (2gh)½, the required height can be calculated. Ultimately, understanding the proportional relationship between height and velocity is key to solving the problem.
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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.
 
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You can do it that way. Note that v = (2*g*h)½

If v ∝ h½ ...

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

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