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## Homework Statement

A projectile is fired from a gun (adjusted to give maximum range) with velocity [tex]v_{0}[/tex]. The projectile passes through two points at a height h. The problem asks us to show that [tex]d=\frac{v_{0}}{g}\sqrt{v^{2}_{0}-4gh}[/tex]

where d is the distance between the two points at height h.

## Homework Equations

[tex]r=v_{0}t+\frac{1}{2}at^{2}[/tex]

[tex]v=v_{0}+at[/tex]

[tex]x= \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}[/tex]

## The Attempt at a Solution

I was able to get a quadratic function of x:

[tex]0=\frac{g}{v^{2}_{0}}x^{2}-x+h[/tex]

After manipulation using the quadratic formula, all I can see is:

[tex]x=\frac{v^{2}_{0}}{2g}+\frac{1}{v_{0}}\sqrt{v^{2}_{0}-4gh}[/tex]

Which just

*looks so close*but I'm killing myself in trying to see how it is either (1) wrong or (2) able to be simplified.

**EDIT:**[tex]x=\frac{v^{2}_{0}}{2g}+\frac{1}{2gv_{0}}\sqrt{v^{2}_{0}-4gh}[/tex], sorry.

Help?

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