Solve the following problem using MATLAB's built-in functions for solving ODEs:

A small rocket having an initial weight of 3000 lb (including 2400 lb of fuel), and initially at rest, is launched vertically upward. The rocket bums fuel at a constant rate of 80 lb/s, which provides a constant thrust, T, of 8000 lb. The instantaneous weight of the rocket is w(t) = 3000-80t lb. The drag force, D, experience by the rocket is given by D = lb, where y is distance in ft, and g = 32.2 ft/s ² . Using Newton's law, the equation of motion for the rocket is given by: Determine and plot the position, velocity, and acceleration of the rocket (three separate figures on one page) as a function of time from t = 0, when the rocket starts moving upward from rest, until t = 3. Reduce the second-order ODE to a system of two first-order ODEs.

dy. 0.005g(- dt w dy 9 dt = T-wD