# Finding muzzle velocity using range and height of barrel

1. Jun 13, 2010

1. The problem statement, all variables and given/known data
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.

2. Relevant equations
Let v0 = Initial muzzle velocity
o = angle of barrel = (33.82 Degrees if this is neccessarY)
Height of barrel = h = 1.13m

3. 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 travelled = 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.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jun 14, 2010

### Andrew Mason

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