Project 13B: Winners of Choose Your Adventure

Your group is to design a problem that incorporates the three main principles the p-cubed course has focused on:

After last week's massacre, all of the physics students have rejoiced that their TA's are dead. They move away to the Appalachian mountains where they plan to live out a long physicsless life. Suddenly, alarm sirens go off and the students rush to the edge of their mountaintop community to see what the fuss is about. That's when they noticed a mob of TA zombies running at them. Lilly, (one of the craziest zombies) is limping because of her human dance injury so she talks to all of the other TA zombies and they decide (after discussing the physics of things and giving each other notes on their conversation skills (Yannis got a 4/4 obviously)) that they should combine their bodies into one mega zombie with a velocity of 10m/s. Luckily a student remembers that they have a professor Irving locked away in their mountain jail where they only feed him the leftover Halloween candy he had brought into class and play the song the class voted as #1 on repeat 24/7. With Irving's help, the students come up with a plan to kill the zombies with a flaming ball of clay. Luckily we have a catapult on our mountaintop. Irving gives us a PowerPoint slide recommending us to treat it as a massive rod with a boulder on the end (moment of inertia = $mL^2/3 + (2/5mr^2 + mL^2}$. The rod is solid. The clay boulder we are shooting is flaming and pink. The catapult is loaded using a spring/crank system (see diagram) and the clay ball is launched when the catapult arm reaches its highest point.