How Can I Derive x = (sqrt(2h/g))v from h = .5gt^2 and x = vt?

[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!

 

[blue88]

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

 

[TD]

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?

 

[TD]

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

 

[quantumdude]

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

 

[quantumdude]

The complete solution is right here in this thread.