Projectile motion - horizontal seperation of two points

[hqjb]

Homework Statement

A projectile is fired with velocity v0 and passes through two points, both a distance h above the horizontal. The angle of the barrel of the gun is adjusted for the maximum range, find the horizontal separation of the two points.

Homework Equations

Max range for projectile motion = $\frac{v_0^2}{g}$

The Attempt at a Solution

I try to find the "initial velocity" at height h and sub into the above equation.

$v_{fy}^2 = (V_0\sin 45)^2 - 2gh$
$v_{fx}^2 = (V_0\cos 45)^2$
$\sqrt{v_0^2 - gh}$
$R = \frac{V_0^2 - 2gh}{g}$

My answer is wrong of course...
Blah, its a multiple choice question and don't think it should take so many steps. Any hints?

 

[voko]

To find the separation between these two points, you need to know the time difference. Can you relate time to elevation h?