After following this thread for a couple days, I brought the question up to a friend at lunch. He is a firearms instructor for local law enforcement.
He surprised me with a different,“back of the envelope” analysis. To paraphrase:
“When do we see a person knocked backwards for a significant distance? When a running back hits a defender in open field after building up speed. A RB may be about 240 pounds moving at 15 mph. Take a 12 pound bowling ball (1/20 the mass) and move it at 300 mph to get the same total force. I’m sure you could easily do this with air pressure. Not sure how to make it man-mobile, though.”
300 mph is about 440 fps, which is less than half as fast as a handgun bullet. I have NO idea how much air pressure would be required.
Question answered, so just a comment. The amount of poor firearm handling and effects are legion in film. I know they hire gun experts, but seem to rarely listen to what they say. The only realistic films show people dropping like bags of wet cement when killed.
