Find Initial Velocity of Projectile Fired from Above Ground Level

[dotachin]

I'm currently doing a Lab in my University Physics class to calculate the initial velocity of a ball right as it's fired from a cannon. I'm not particularly looking for the answers, just the equation needed (i think I copied the equation from the professor incorrectly).


Here's what I have:
vnought = v/cos(θ)(g/2(xtan(θ)+H)), x= range, H = height off the ground. v is what i believe i copied down wrong. the issue I'm running into is we didn't take velocity data, only the range, height off the ground, and angle of the cannon.

my question is a) is this right and I'm just blanking out in a way to find the v? or b) what is the correct equation


I have some sample data if it would help with calculations. we did three shots and averaged them together for a general range.
trial 1: θ=5°, xavg = 5.13m, H= 1.0m

 

[jbsteele]

trial 2: θ= 10°, xavg = 11.0m, H= 1.3mtrial 3: θ = 15°, xavg = 18.9m, H= 0.7m The correct equation for calculating the initial velocity of a ball fired from a cannon is: vnought = (2*g*x*tan(θ)) / (cos(θ) * (xtan(θ)+2H))where g is the acceleration due to gravity, x is the range, θ is the angle of the cannon, and H is the height off the ground.