Mary is an avid game show fan and one of the contestants on a popular game show. She spins the wheel and after 1.5 revolutions, the wheel comes to rest on a space that has a $1,500.00 prize. If the initial angular speed of the wheel is 4.05 rad/s, find the angle through which the wheel has turned when the angular speed is 1.90 rad/s.

At a certain instant after jumping from the airplane a, a skydiver b is in the position shown and has reached a terminal (constant) speed vb = 52 m/s. the airplane has the same constant speed va = 52 m/s, and after a period of level flight is just beginning to follow the circular path shown of radius ρa = 2330 m. (a) determine the velocity and acceleration of the airplane relative to the skydiver. (b) determine the time rate of change of the speed vr of the airplane and the radius of curvature ρr of its path, both as observed by the nonrotating skydiver.