Problem:

This problem is based on the Red Bull minidrome events. The specs for the minidrome are given on this page. Given that the total length of the track is 25 m and is generally symmetric which suggests that the end curves have an effective radius of 2 m

Given that the desire is for there to be limited lateral friction on the tires what is the ideal speed for a rider on the steepest part of the corner where it is banked at 42 degrees? What is the necessary radius of the path of the rider when they exit the corner and the bank angle is only 22.5 degrees (also without friction)? Your answers will, of course, be based on a crystalline freebody diagram and the clear presentation of a Newtonian analysis.