You are designing the section of a rollercoaster ride shown in the figure. Previous sections of the ride give the train a speed of 10.7 m/s at the top of the incline, which is h = 39.1 m above the ground. As any good engineer would, you begin your design with safety in mind. Your local government's safety regulations state that the rider's centripetal acceleration should be no more than n = 1.69 g at the top of the hump and no more than N = 5.85 g at the bottom of the loop. For the initial phase of your design, you decide to ignore the effects of friction and air resistance (figure not shown to scale) (figure in image)
What is the minimum radius hump you can use for the semi-circular hump?
What is the minimum radius loop you can use for the vertical loop?