A rocket body of mass M will fall out of the sky with terminal speed vT after its fuel is used up. What power output must the rocket engine produce if the rocket is to fly
(a) At its terminal speed straight up;
(b) At three times the terminal speed straight down? In both cases assume that the mass of the fuel and oxidizer remaining in the rocket is negligible compared to M. Assume that the force of air resistance is proportional to the square of the rocket’s speed