# What is the significance of sqrt{2gh} ?

1. ### acspin

6
Hi, I'm not sure how to word my question, so I will just state it upfront.

What is the importance of $$\upsilon$$ = $$\sqrt{2gh}$$ in physics?

I've seen it in escape velocity problems, though with an R instead of h. I've seen it with conservation of momentum applications, and it's similar to PE = mgh. Yesterday my professor was discussing Bernoulli's equation and this equation came up again.

I was just wondering how it can be applied to so many different situations...

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3. ### tiny-tim

26,055
Welcome to PF!

Hi acspin! Welcome to PF!

(have a square-root: √ )

It's because v2 is KE per mass.

Whenever KE + PE =constant, you'll have equations involving v2 = PE/m, which in some cases is gh.

As to Bernouli's equation, that's just conservation of energy applied to a fluid, and both KE and PE appear in it.

4. ### GRDixon

250
When acceleration is constant, say along the x-axis, then it is necessarily true that

v^2=2ax. (where v at time t=0 is zero).
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