Ignoring air resistance (which you really shouldn't, especially not when you're talking in the thousands of meters per second), you need to launch something at around 1400m/s get it to 100km high "suborbital". You need to launch it over 8000m/s to get it into orbit. In 2022, Spinlaunch were getting to ~450m/s, but that was two years ago and maybe they've improved.

Now, 1400m/s is in the neighborhood of a tank cannon, which is doable. But 8000m/s on the surface, or about 29.000 kph, is about mach 23. That's like running smack into a brick wall of air, every millisecond. And in reality, you need MUCH more speed, because you're shooting at a much shallower angle, so there's a lot more air to get through.