A roller coaster consists of a large hill, followed by a loop with a radius of 20 meters. The roller coaster car starts at the top of the hill, gains speed as it rolls down, and then travels around the loop, starting at the bottom and turning the riders upside down at the top. You may neglect friction and air resistance. (For clarification: the bottom of the hill is at ground level, as is the bottom of the loop).
a. How high must the hill be to ensure that the car doesn't fall off the loop? [Hint: first, find symbolically the minimum velocity required to complete the loop. Substitute numbers at the very end.]
b. Why does the exact shape of the hill not matter?