Note: Acceleration clue to gravity g = 9.81 mis', yo= height, V0 Initial velocity You see a shot putter before it is thrown! a) Set up the equations of motion (differential equations) for the sphere, taking friction into account b) The world record for women is 22.63 m in shot put. Try to model this record as part of an energy analysis for the sphere. Formulate three basic assumptions! Why is the optimal launch angle at a = 40\"? Is the system uniquely determined with the parameters. Important model parameters: Height of the athlete: 1.86mi; Ball mass: m = 4kg. V initial = 14.2 mfs c) The energy expenditure measured in the athlete is W = 5950 J. Compare your calculated value with the athlete's energy expenditure and interpret the result