Meriam, Kraige & Bolton — Kinetics of Systems of Particles: Problem 4_85

4/85 A two-stage rocket is fired vertically up and is above the atmosphere when the first stage burns out and the second stage separates and ignites. The second stage carries 1200 kg of fuel and has an empty mass of 200 kg. Upon ignition the second stage burns fuel at the rate of 5.2 kg/s and has a constant exhaust velocity of 3000 m/s relative to its nozzle. Determine the acceleration of the second stage 60 seconds after ignition and find the maximum acceleration and the time \( t \) after ignition at which it occurs. Neglect the variation of \( g \) and take it to be \( 8.70 \text{ m/s}^2 \) for the range of altitude averaging about 400 km.