What is the Maximum Range of a Fired Shot from a Launcher?

[AdsBerger]

Homework Statement

A launcher fires a ball that weighs 30kg straight up to a height of 300m. What is the maximum range of the ball could be fired at?

Homework Equations

V^2 = V^2-2(a)(d)
R = ( V02 Sin2θ ) / g

The Attempt at a Solution

To find the maximum range i know that it has to be fired at a 45° angle.
It is in our energy and momentum etc. unit, practice so I am guessing equations relevant to that is what i must use.
I used this equation to find the Velocity when fired straight up. Which i got 76.68 m/s. Which if i drew a triangle to show the projectory, would be my height. I then used 76.68SIN(45°) to get 54.22 m/s. Which is my x & y velocity. Then i used the range formula to get 300 m.
Is anything wrong with my work, shouldn't it be a different answer than 300m.

 

[nasu]

What is the initial speed?
What is the expression for the maximum range?
You don't really need to calculate the components of the velocity if you already know the formula for the range.

 

[AdsBerger]

So the initial speed no matter the angle you fire at will all be the same?

 

[AdsBerger]

I believe i ended up getting it. answer 600m

 

[nasu]

Yes, this looks OK.