5. One of the goals of the US Aerospace industry is to develop the ca pabilitjyr to put payloads into orbit at the cost of $1 per 1b. Various strategies can be considered to accornplish that. Consider the design of an optimal two- stage rocket with a liquid-prOpellant rst stage and a solid-propellant sec0nd stage. The rocket will he used to launch payloads for the space station up to 500 kg in mass into near-earth orbit, requiring a An : 9 km/s. The two stage characteristics are: stage no. I510, s 5 1st 350 0.2 2nd 230 0.15 (a) What is the total mass at liftoff and what are the masses of each stage? Use the method of Lagrange multipliers applied to the following equation to answer these questions, What value of 0: do you obtain? Hint: Then to nd the masses, evaluate the payload ratios, 0:16,: RI: 2 aaaa Also, in the class notes R; was denoted as Ag. (b) It the maximum accelerations are to be limited to 1090, what are the maximum propellant mass ow rates for each motor stage? Assume that the largest acceleratiOn for each stage will occur at burnout. (c) Assume constant propellant mass flow rates at the maximum possible values. What is the thrust/weight ratio at liftoff? At second ignition? What are the burn times for each stage