Quote from Whyrainfalls;123487:
Seeing as he's in his home with no wind, I don't think he'd want to waste any gunpowder when the trajectory is just a simple kinematics problem.
Using trial and error for something as simple as this would be like using guess and check for arithmetic problems.
If he did use trial and error at all, he predicted the general location, then made small adjustments.
You also have to factor in changes in the cannon after it having been fired several times, recoil, and more that I haven't named. It's not too hard to find the general trajectory of the cannon, so of course he would have just made small adjustments. Although you have to realize that since the cannonball isn't secured to the table, it won't always hit the exact same place, as shown with the computer.
The more science you learn, the more you realize that it isn't very exact at all.