Let the rocket of Fig. E3.12 start at z = 0, with constant exit velocity and exit mass flow, and rise vertically with zero drag. (a) Show that, as long as fuel burning continues, the vertical height S(t) reached is given by S = Ve Mo/m ζ in ζ−ζ +1 where ζ = −1 mt/mo (b) Apply this to the case Ve = 1500 m/s and Mo = 1000 kg to find the height reached after a burn of 30 seconds, when the final rocket mass is 400 kg.