Finding muzzle velocity using range and height of barrel

[physicsisrad]

Homework Statement

Ok, so pretty much, I built an air cannon for my physics assignment. I need to determine the muzzle velocity. I know the angle of the barrel, the height of the muzzle about the ground and the distance the projectile covered. I fired projectile at multiple pressures in order to determine the effect of pressure of muzzle velocity. I am ignoring drag and friction for these equations.

Homework Equations

Let v0 = Initial muzzle velocity
o = angle of barrel = (33.82 Degrees if this is necessary)
Height of barrel = h = 1.13m

The Attempt at a Solution

Total time of flight= t = v0sin(o)/9.8^2+ (v0sin(o)^2/9.8^2 - 2*h/9.8)^0.5
Distance traveled = v0cos(o) * t
= v0cos(o) * (v0sin(o)/9.8^2+ (v0sin(o)^2/9.8^2 - 2*h/9.8)^0.5)
I need the rearrange this equation so v0 is the subject so I can implement this in an excel spreadsheet as I have literally hundreds of these to determine.

 

[Andrew Mason]

What is your question?

If you are trying to find muzzle velocity, you have to solve these equations for time:

(1) $$x = v_0\cos\theta t$$

(2) $$y = v_0\sin\theta t - \frac{1}{2}gt^2$$

Find the muzzle velocity by substituting t into (1).

AM