A "home-made" solid propellant rocket has an initial mass of \(9 \mathrm{~kg}\); \(6.8 \mathrm{~kg}\) of this is fuel. The rocket is directed vertically upward from rest, burns fuel at a constant rate of \(0.225 \mathrm{~kg} / \mathrm{s}\), and ejects exhaust gas at a speed of \(1980 \mathrm{~m} / \mathrm{s}\) relative to the rocket. Assume that the pressure at the exit is atmospheric and that air resistance may be neglected. Calculate the rocket speed after \(20 \mathrm{~s}\) and the distance traveled by the rocket in \(20 \mathrm{~s}\). Plot the rocket speed and the distance traveled as functions of time.