Consider launching a satellite into orbit using a single-stage rocket. The rocket is con- tinuously losing mass, which is being propelled away from it at significant speeds. We are interested in predicting the maximum speed the rocket can attain.2 3. Assume the rocket of mass m is moving with speed 11. In a small increment of time At it loses a small mass Am p, which leaves the rocket with speed u in a direction opposite to 1). Here, Amp is the small propellant mass. The resulting speed of the rocket is v + Av. Neglect all external forces (gravity, atmospheric drag, etc.) and assume Newton's second law of motion: force = E(momentum of system) where momentum is mass times velocity. Derive the model dv _ (1?) dm d1 _ m d: where c = u + v is the relative exhaust speed (the speed of the burnt gases relative to the rocket). b. Assume that initially, at time t = 0, the velocity v = 0 and the mass of the rocket is m = M + P, where P is the mass ofthe payload satellite and M = EM + (1 E)M (0 <: e is the initial fuel mass em plus of rocket casings and instruments. solve model in part to obtain speed m v="cln" c. show that when all burned given by v-="_cln1-" where p ratio payload mass. d. find u_ if c="3" kin f3 are typical values satellite launchings. e. suppose scientists plan launch a circular orbit h km above earth surface. assume gravitational pull toward center newton inverse square law attraction: ymme re y universal constant mt. radius earth. this force must be balanced centrifugal mvz satellite. what attained into an surface from your computation can singlestage height>