Solve the wave equation utt = uxx subject to boundary and initial conditions of the form u (0, t) = 0 ux (1, t) = 0 u (x, 0) = 0 ut (x, 0) = 1. This would describe a string that is attached to something on the left side, connected to a frictionless hoop/rail system on the right side, and suddenly hit from below in such a way as to impart a constant velocity to the string.

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.