Question 1: A rocket having mass M is launched vertically with a trust force 7. a) Maximum trust force is 1000 N the trust actuator, simulate and analyse (15 points). b) Assume that the mass of the rocket M = 100 and the gravity g = 9.81 are constant. and its 99% can be produced in 10 seconds. Model Derive the dynamic model of the rocket with the trust actuator, simulate and analyse (15 points). 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). d) The mass of the rocket converges to M=70 in 1000 seconds due to fuel consumption where the g becomes zero at the space. Modify the model in 1.b, simulate and analyse (15 points).