Problem

An airplane is about to crash-land with a vertical component of speed υ0 = 2 ft/s and zero...

An airplane is about to crash-land with a vertical component of speed υ0 = 2 ft/s and zero roll, pitch, and yaw. Determine the vertical component of velocity of the center of mass of the airplane G as well as the airplane’s angular velocity immediately after touching down, assuming that (1) the only available landing gear is rigid and rigidly attached to the airplane, (2) the coefficient of restitution between the landing gear and the ground is e = 0.1, (3) the airplane can be modeled as a rigid body, (4) the mass center G and the point of first contact between the landing gear and the ground are in the same plane perpendicular to the longitudinal axis of the airplane, and (5) friction between the landing gear and the ground is negligible. In solving the problem use the following data: W = 2500 lb (weight of the airplane), G is the mass center of the airplane, kG = 3 ft is the radius of gyration of the airplane, and d = 5.08 ft.