In a jet airplane, the kinetic energy imparted to exhaust gases is wasted as far as propelling the airplane is concerned. The useful power is equal to the product of the force available to propel the airplane and the speed of the airplane. If v is the speed of the airplane and u is the relative speed of the expelled gases, show that the mechanical efficiency of the airplane is η = 2v/(u + v). Explain why η = 1 when u = v.