This is a fun lesson I've been doing for a couple years now with my Algebra 2 class. This post will briefly explain what the project is about and show how the catapults were made. Part 2 will include the actual project packet, and go into more detail about how it all works.
Each group of students (2-3) gets a small catapult, and shoots M&Ms from it while it is on the ground. They measure how far each shot goes and how long it is in the air and use that to figure out how far the catapult will fire when they place it up on a desk. They place a target where they think their projectile will land, and get points based on how accurate they are. I check in with each group regularly so they aren't getting too far off course. It's probably my favorite project because it takes a large number of the things we've done in the chapter on parabolas and puts it all together, in a "real life" situation. (While firing M&Ms doesn't have much of a purpose, it's pretty easy to get them to understand the correlation to ballistics)
Unfortunately this project does require some setup (making the catapults), but it shouldn't take too long. I bought popsicle sticks, a few small pieces of wood, wood glue and some small clothespins at the local crafts store and used some scissors and masking tape to make this:
If you have Google Sketchup you can see my model of it here.
The plans are (I hope) pretty self explanatory from the pictures above. The base was a small piece of hard wood I also found at the craft store. The clothespin sits on a platform made of four popsicle sticks cut up with scissors. The basket to hold the candy is made out of masking tape. I added the guide rails on the sides to help with accuracy, in the picture directly above I removed one so that you could see the interior better. This year I was considering changing the plans to allow some sort of button to fire it to improve accuracy, but overall if the students were careful they came out with excellent results.
Stay tuned for part 2 which will include the actual project the kids do!