2. In this question you will investigate the dynamics of the long jump event, using the projectile motion equations to compare the solutions with and without aerodynamic drag. In a search for typical parameter values, I have been able to nd the following partial list for elite male/'female long jump athletes: Parameter Men Women Body mass, m (kg) W3 62 Takeoff velocity, VD [m/s] 9.4 8.6 Body height. (m) 1.85 1.70 Drop in CM, h {m} 0.6 Frontal body area, A (m2) 0.5 Drag-towcight ratio, E 0.03 (a) Before starting, determine estimates of the 3 blank entries in the table for female long jumpers, namely: the drop in centre of mass from takeoff to landing (h); frontal body area (A); and dragtoweiglit ratio (6). Keep in mind the following 0 An estimate of the drop in CM (h) for women can be found by taking the men's value and scaling it by the same ratio as body height. 0 Body crosssectional area clearly also depends on height, so you can estimate the women's value of A using the same sealin 0 Finally, recalling that drag force is proportional to area. A, it makes sense that the drag toweight ratio 6 for women should also be scaled by the same factor. (b) (d) Start by considering the case that drag is negligible, and use the projectile motion equations we derived in class to determine the optimal takeoff angle 6' and range R for both men and women. Consider only the distance travelled by the athlete's CM, and neglect any corrections due to foot placement at takeoff or landing. Then incorporate aerodynamic drag and nd the corresponding optimal solution when drag force is proportional to the square of speed [that is, FD = k'ug}. Since there is no analytical solution available for this case, modify the Matlab code quaddragnn posted on Canv to instead run some longjumper simulations. Determine the optimal jump distance for both men and women manually, by setting the other parameters and then varying the take01:1r angle until you obtain the maximum range within an accuracy of :|:U.5 cm. Compare your results from parts b and c (with and without drag) and comment 011 the appropriateness of the zercsdrag assumption in modelling the long jump event