Question 1: A rocket having mass M is launched vertically with a trust force 7. b) Assume that the mass of the rocket M = 100 and the gravity g = 9.81 are constant. Derive the dynamic model of the rocket with the trust actuator, simulate and analyse c) Add air friction b=0.9, air inertia k = 0.4 and the wind n=0.1 into the model in 1.b. Simulate and analyse (15 points). Question 2: Consider the rocket model in 1.c by considering the thrust actuator dynamics, but ignoring the gravity stemmed dynamics. It is desired to design a rocket that will reach 1000 km in 2000 seconds with less than 5% overshoot. a) Design a stabilizing controller, simulate and analyse (15 points).