1. A simple model of rocket propulsion Let us consider a mass m vertically going up with the velocity v under the downward gravity g at time t, where we set positive direction upward. Within a time interval t t + At, it releases Am amount of hot gas with relative velocity ve of the exhaust velocity with respect to the rocket m - Am: m - Am 19/4 m ve Am (1) Our goal in this question is to derive the following acceleration of the rocket: a = - Igl (2) m dt (a) If we consider the gas and the rocket as a single two-body system, gravity is the only external force on it. Find the change in momentum of the system. (b) Recalling Newton's second law in terms of momentum difference, write the equation of motion. In particular, determine the total force on the system. (c) Discuss the motion of the center of mass. (If you write EoM in lb, find the acceleration and you will see.) (d) Let us look at each part. If the rocket m - Am kicks the gas Am, the gas receives some downward force, say F = - [,| 0 be the upward force acting on the rocket m - Am. The total force on the rocket m - Am is the sum of , and the gravity. If we write