[DonRotolo]

I think a rotary actuator may not have enough "oomph" for you. Try it anyway instead of doing nothing. A linear piston can fire a ball pretty far, but there are some trade-offs to consider.

Small diameter pistons tend to fire faster, because the limiting factor is how much air you can pass through those hoses and valves, and smaller pistons use less air.

But they also push with less force. In the extending direction, for example, a 3/4" bore piston can generate about 26 pounds of force using 60 PSI. (More details are in the pneumatics manual)

Large pistons are slower (more air) but stronger (look up the force for a 2" bore piston!).

One technique is to use a lever with a pivot to multiply the speed at the expense of force. Using a 10 inch bar as an example, push at one end at 20 Feet per second, have a pivot at 2", the far end moves at ((8/2)*20)=80 FPS, with 2/8 (1/4) the force. The challenge is here is to manage the size, strength and friction.

Another technique is to pre-charge the piston: Imagine a 10 inch long piston, held in place somehow with 5 inches extended. Charge the backside of the piston with 60 PSI. Then, release the rod so it can extend the full 10 inches - it'll come out fast and strong. The design challenge here is reliably and safely releasing the rod that is under a great deal of force (obviously some kind of mechanism is necessary)

These challenges have been solved in may ways by others. There are also other ways of "skinning that cat" - but telling you everything would take out the fun, wouldn't it?

Good luck, we're all wishing you the best.