Arocket accelerates by burning its onboard fuel, so its mass decreases with time. suppose the initial mass of the rocket at liftoff (including its fuel) is m, the fuel is consumed at rate r, and the exhaust gases are ejected with constant velocity ve (relative to the rocket). a model for the velocity of the rocket at time t is given by the equation v(t) = −gt − ve ln m − rt m where g is the acceleration due to gravity and t is not too large. if g = 9.8 m/s2, m = 29,000 kg, r = 140 kg/s, and ve = 2,800 m/s, find the height of the rocket one minute after liftoff. (round your answer to the nearest whole meter.)

Simon is writing a story about an astronaut whose spacecraft has been boarded by space pirates. the astronaut has her lucky penny in her hand behind her back as the space pirates break into the control room. she has just locked the controls so that the ship is accelerating in the direction of the control room’s ceiling. simon wants the astronaut to use the penny to hit a button on the control panel to turn off the lights and escape. the button is located a short distance behind and below the astronaut’s hands. how should simon use the theory of relativity to describe what the astronaut must do in order to hit the button?