Great question. I cant find a direct explanation, so I will provide an explanation based off of the then concurrent science and give you sources to how I determined my conclusions.

Prior to the modern determination of how forces work, there was a scientific concept called Impetus. Impetus functions similarly to Linear Momentum in that it describes an object's trajectory as travelling in a straight line after enacted upon an outside body; it was calculated by 14th centurt Philosopher, Jean Buridan, as Impetus=Weight*Velocity. But unlike Momentum which does not change unless further acted upon, Impetus always decays after it is transferred. And exponentially too.

As an example, imagine what happens to your cannonball with an understanding of modern physics. If shot horizontally, with 0 vertical vector, its path begins to decay immediately and we get a nice smooth parabolic path. We blame this on gravity and its force pulling the cannonball to earth. At the same time, the cannon moves backward, resisted by friction and possibly gravity based on its base design.

Lets reimagine our scenario with Impetus in mind. In In Phys., John Philoponus says that a stone (our cannonball) will take upon itself Impetus (incorporeal motive enérgeia) from the outside body. Once that Impetus runs out, it will fall to the ground. So instead of the nice parabolic curve, you would get a rough L-Shaped curve. Our cannon still moves backward, but we assume that it is because the explosion inside of it also imparted Impetus to it. The cannon stops moving quickly because its already touching the ground and its fairly heavy.

Edit:I had more, but then I realized I was going very far off track of the question.