Range of projectile traveling through two points at same elevation

[UrbanXrisis]

"A projectile is fired with an initial velocity V_o such that it passes through two points both a distant h above the horizontal. Show that if the gun is adjusted for a maximum range the separation of the potins is?"

my work is http://home.earthlink.net/~suburban-xrisis/projectile.pdf"

does it look correct?

 

[Meir Achuz]

h/A does NOT equal tan 45. Just look at your picture to see this.
Find h in terms of A by using the eqs. A=v_0 t cos45 and
h=v_0 t sin45-(1/2)gt^2.

 

[UrbanXrisis]

I'm not sure why they would not be equal.

Opposite/Adjacent = tan(theta)

The side opposite to the angle is h
The side Adjacent to the angle is A

so the equation should read: tan(45)=h/A

and why would I want to get h in terms of A? Dont I want A in terms of h?

I made up the variable A so I that I could get A in terms of h and subtract it from the max range.