Organizing officials from the X-games hear that you have a knack for applied problems. They fly you from Cleveland to San Diego to help design the half-pipe for the skateboard competition. This year they are considering building a half-pipe which maximizes contestants' speed (assume only gravity is at work here and there is no friction or air resistance). What shape do you suggest to them? They will need justification (mathematically) and visually so you should include a plot (use MATLAB). Using your suggested shape, calculate the time it takes for a contestant starting at rest at the top of the half-pipe to get to the very bottom. Also, calculate the time if the contestant starts half-way up the pipe. Do you notice anything strange? Finally, find out if real half-pipe designs follow your suggestion. Organizing officials from the X-games hear that you have a knack for applied problems. They fly you from Cleveland to San Diego to help design the half-pipe for the skateboard competition. This year they are considering building a half-pipe which maximizes contestants' speed (assume only gravity is at work here and there is no friction or air resistance). What shape do you suggest to them? They will need justification (mathematically) and visually so you should include a plot (use MATLAB). Using your suggested shape, calculate the time it takes for a contestant starting at rest at the top of the half-pipe to get to the very bottom. Also, calculate the time if the contestant starts half-way up the pipe. Do you notice anything strange? Finally, find out if real half-pipe designs follow your suggestion