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PROBLEM 8. The total weight of space shuttle including its payload mass and the empty external tank, and its empty two solid rocket boosters is mo = 428,100 lb. It is known that the external tank and the two solid rocket boosters initially holds my (0) = 3,728,875 /b of fuel (that is the total weight of solid fuel plus liquid oxygen and hydrogen). The shuttle consumes its liquid and solid fuels at a constant rate of dy = 14,300 lb/s. Also, it is known that the shuttle thrust force is Fe = 400,000 lb. (a) Use the Newton's 2nd law below to find the second order differential equation that describes the vertical position y of the space shuttle as a function of time. The shuttle is launched vertically upward from the ground as shown below, with the positive direction upward and the air resistance is ignored. The Earth's gravitational acceleration on its surface is g = 32.2 ft/s and its radius is R = 4000 miles. Ftotal (t) = = [m(t). v] F Where, thrust - Frotar(t) is the net force acting on the space shuttle that is the difference between thrust force F, and gravitational force Fo. - m(t) denotes the total mass of the rocket at time f given by 10 Fgravity - Fg m(t) = mo+ my(t) - mo is the constant mass of the shuttle including the mass of payload, the empty external fuel tank and rocket boosters. of Earth - my(t) is the variable amount of liquid and solid fuels given by my (t) = -dyt + my(0) (b) Find the escape velocity from the earth when shuttle is non-propelled, vo