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 burns 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, experienced by the rocket is given by $D = 0.005g(\frac{dy}{dt})^2$ 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
$\frac{w}{g}\frac{d^2y}{dt^2} = T - w - D$.
Write a MATLAB implementation that applies a fourth order Runge-Kutta method to solve this initial value problem for $t \in [0, t_f]$. 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 $t = t_f$. Any unknown values are to be taken from the user.
