12. (12 points) In a freak hot tub accident you find yourself sent back in time to medieval days. To avoid death you proclaim you possess magical powers and can correctly choose the necessary ideal spring for their catapult to fire upon any distance. They setup a demonstration and ask you to hit a target 200 m away with a 100 kg boulder. What is the spring constant, in N/m, of the spring you would use? Assume the spring compresses the full distance d before the launch and that it leaves the catapult at a height h above the ground. Neglect air resistance. d=4m 0-30 Ax - 200 m m = 100 kg K h 4x