In the video above, I show how to calculate the cannon velocity.
In my experiment, I used
receipt Impact paper so that when the ball lands on the top
carbon paper, a mark is made on the paper beneath it. I could have used a
carbon paper sheet, but I would have to supply the paper beneath it.
In this experiment the cannon velocity was 4.3 m/s. If I remove the barrel
(used to make the ball travel more accurately), the velocity would be greater.

The way you determine the cannon velocity is dependant on
the time it takes to drop the projectile and the distance
the projectile is able to shoot. First you shoot the cannon
at a horizontally zero degree angle. Then you measure the
distance from the base of the cannon to where the projectile
first made impact with the surface. That distance can be called
\(x\). Next you need to calculate the time. A projectile motion
formula is

$$ y - y_o = v_o t + {g t^2 \over 2} \tag{1}$$

If you consider that \(y-y_o\)is your height \(y\) and if you
consider that \(v_o\) is zero since we are shooting horizontally,
you can say that

$$ y = 0 + \frac{gt^2 }{2} $$

\(y-y_o\) and \(y\) = height, \(v_o\) = zero, \(g\) = gravity,
\(t\) = time, \(v\) = velocity. When you solve for time \(t\),
you'll have the equation of

$$t = \sqrt {2y \over g} \tag{2}$$

If we consider the projectile formula for horizontal velocity,
we have:

$$ x - x_o = v_o t + {a t^2 \over 2} \tag{3} $$

If we consider \(x - x_0\) is distance \(x\) and since we have
no horizontal acceleration or deceleration, the above formula simplifies to: