The X-15 rocket-powered plane holds the record for the fastest speed ever attained by a manned aircraft at 2020 m/s. At this speed, by how much is the 15.5 m-long aircraft length contracted? Hint: use binomial approximation

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.