Project 14: Part B: Sharks!

Your team is traveling across the Pacific Ocean on a tug boat, and you get a call that someone's boat has broken down, leaving them surrounded by great white sharks. You have a catapult with a steel ball (10 kg) loaded in it, and clay balls (5 kg each). The catapult is 8 m long, has a mass of 5 kg, and rotates about its center. The strongest person on your team is able to throw the clay balls at a speed of 47 m/s. Your mission is to save the people on the stranded boat by hitting the sharks in the snout with the steel ball, and to make sure that the sharks recoil with a great enough speed after being hit by the steel ball that they won't want to come back. Better hurry before it's too late and the sharks attack!

First, using angular momentum conservation for the collision between the clay ball and the catapult:

$$L_{i, clay}=L_{f, clay, steel, catapult}$$ $$m_{clay}v_{i,clay}R_{catapult}=I_{tot}w$$ $$m_{clay}v_{i,clay}R_{catapult}=(m_{clay}R_{catapult}^2+m_{steel}R_{catapult}^2+1/12*m_{catapult}L_{catapult}^2)w$$