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 (mass of 50kg). Luckily we have a catapult on our mountaintop. Irving gives us a PowerPoint slide recommending us to treat it as a massive rod (mass of 10kg) with a boulder on the end (moment of inertia = $(mL^2)/3 + {2/5mr^2 + mL^2})$. The rod is solid and has a length of 10m. The clay boulder we are shooting is flaming and pink. The catapult is loaded using a spring/crank system (see diagram, k of spring 453 kgm/s and its maximum stretch is 12) and the clay ball is launched when the catapult arm reaches its highest point. If the mountain is 80 meters tall how far away from the mountain will the flaming ball hit?

Once you fire the ball your notice that your calculations were slightly off and you have hit the top of the combined zombie pile resulting in the creation of a boulder made up of zombies and flaming clay. The flaming clay hits at a radius of 3m from the center of the mass of the zombies. What was the mass of the zombie pile and what is its final velocity after the clay ball collides with it?