In any case, a very cool project IMHO. I've long wondered how fast modern technology could throw a projectile without resorting to explosives. I now know it can at least be supersonic.
Can it go even faster, though? Is there an even better mechanical design than a slingshot?
Railguns can get projectiles up to mach 8. The magnets at the HLC can get particles pretty close to the speed of light.
I think if you continued with the trebuchet/rubberband approach you'd really only be limited by the amount of tension you'd be able to put your band under. There are probably better materials than rubber.
I think the main stopper for higher speeds would be materials strength, especially with that design relying on a cable, but even so I doubt the limits are anywhere close from what was achieved in this video.
https://en.wikipedia.org/wiki/Trebuchet
https://exarc.net/issue-2018-3/at/traction-trebuchet
This seems like a form of traction trebuchet with traction provided by the elastic.
