Hi, I'm not sure how to word my question, so I will just state it upfront. What is the importance of [tex]\upsilon[/tex] = [tex]\sqrt{2gh}[/tex] 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...
Welcome to PF! Hi acspin! Welcome to PF! (have a square-root: √ ) It's because v^{2} is KE per mass. Whenever KE + PE =constant, you'll have equations involving v^{2} = 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.
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).