This fun project (Part I and Part II) comes from Sean Sweeney. The catapults will take some advance preparation on the part of the teacher. Students work on projectile motion and modelling using quadratic functions.
Sean’s student handout explaining everything is at this link.
I didn’t tag this one for Math 20-2 (Foundations 11). I haven’t tried it in a classroom, but I think it would be too challenging for them. If you use it there and it works, let me know and I’ll update it here.