3. (20 points) On a trip to the amusement park, Mikey decides to ride The Rotor, a spinning ride that is shaped like a long cone (see the picture). You stand pressed against the inner wall, and the ride begins to spin. Once it reaches a certain speed, the floor drops, but the force of the spinning keeps you from falling out. For our example, The Rotor is 10 meters tall, has a bottom diameter of 7 m (where the passengers stand), and the walls are set at 80°. If Mikey weighs 50 kg and there is a coefficient of friction of 0.8 between Mikey and the inner wall, what is the maximum speed (in revolutions per minute) that The Rotor must spin at to keep him from falling out?

Fig: 1

Fig: 2