# Help with a formula

blue88
I need to derive this formula:

x = (sqrt of 2h/g)v

from these two equations:

h = .5gt^2

x = vt

Thanks... just can't figure this out!

stunner5000pt
do you mean $$\sqrt{\frac{2h}{g}} v$$

Start off with the first equation. Replace what can be replaced in this equation. Rearrange and you're there!

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blue88
yes, this is the formula, it was for a lab so we were using x as a distance

Homework Helper
Rewrite the first equation for t, I took the positive root:

$$h = \frac{{gt^2 }} {2} \Leftrightarrow t^2 = \frac{{2h}} {g} \Leftrightarrow t = \sqrt {\frac{{2h}} {g}}$$

All that's left is substituting it in $x = vt$

blue88
but there is no way to combine the x=vt with it?

Homework Helper
That's what you have to do now. Substitute the expression we found for t in the formula x = vt...

Staff Emeritus
Gold Member
Yes, there is. Take $x=vt$ and solve for $t$, then substitute.

Poncho
Are you kiddin' me, buddy? How about $$t = \frac{{x}} {v}$$

blue88
but i need to derive this formula:

x = (sqrt of 2h/g)v

from these two equations:

h = .5gt^2

x = vt

i still don't understand how to do that

Staff Emeritus