This approach does not scale

Every aspect of this cannon requires magic to work. There are just too many presents to deliver. Of course, this is the problem with how Santa operated before the cannon, and you've already said the cannon is magic. But the cannon is so magical that things like 'force' and 'speed' don't really make sense when applied to it.

Number of deliveries

There are about two billion Christians in the world. Very roughly a tenth of that number will be children receiving presents. The number of presents each child receives will of course not be constant (some children want one big ticket item, others want lots of smaller items) but let's assume the cannon's magical delivery protection allows Big Red to fire the cannon once and stack all presents for a given address into a single shot.

Let us further assume everyone lives in a place with a chimney. How many deliveries per person do we need? One per family is a reasonable approximation. We will assume a nuclear family of 4 people, 2 of whom need presents, all serviced by one delivery.

Yes, there are orphanages, hospitals, statistical outlier families with eight kids, etc. but there aren't a lot of them. They will roughly cancel single parent homes, families with one child, etc.

This means each delivery services, on average, two children. Our population estimate of two hundred million happy clients therefore works out to 100M deliveries.

Optimal delivery strategy

Santa wants his cannon to adjust its aim as little as possible. This poses a similar problem as seek time for modern disc-based data storage. Probably the optimal strategy is to deliver presents in strips running from one pole to the other, north to south back up to north, etc, in line with the rotation of the earth. That way he doesn't have to worry about wild divergences in time zones.

Roughly, the rate should work out to approximately one time zone per hour. Regardless of where you are in the world, you can expect your presents to arrive at roughly the same (local) time (say between 2 and 3 AM) because as the cannon delivery pipeline finishes one time zone at 3 AM local time, it rolls over into the next time zone, where it is one hour earlier.

So that means (1/24)th of the total number of deliveries need to be made in one hour (3600 seconds), giving us a final answer of approximately 1160 deliveries per second.

It just doesn't work

Firing a cannon 1160 times per second is going to destroy the cannon. Adjusting its aim 1160 times per second isn't much better. Loading the cannon in less than a microsecond is just silly. You may as well just give up and say "It's a magic cannon, it works very well, thank you very much."