I had to build one once for a physics class. I wouldn't recommend what my partner and I did though, but it was definitely fun. We obtained a large drum that was used to block off parts of the road from a junkyard and cut it in half to fill it with water. We took a gift certificate to menards and got a few strong metal pipes and some boards, and then, proudly refusing to use math or calculations whatsoever we created a 7.5 foot trebuchet that could launch things almost a football field away. We usually fired pop cans, as a tennis ball would just get caught in the winds.
We hauled it to school on the back of a boat trailer and set it up. We fired a pop can, but it flew off the trebuchet backwards and landed on top of the 3 story school. It was probably one of the most fun creations we've ever made. We also did it without spending any money.
However, we got a C, because the assignment was very similar to yours. We just wanted to build a massive one for the hell of it. Nonetheless it was pretty impressive as it did shoot forward a few times as well, though using a tennis ball it only ended up flying up into the air at a high arc, getting caught by the wind, and then flying back into the teacher's parking lot.
Nontheless, it was great fun and I still remember making it, unlike many other things from physics.
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