Neglecting air resistance, what speed would a vertically directed rocket attain in \(5 \mathrm{~s}\) if it starts from rest, has initial mass of \(350 \mathrm{~kg}\), burns \(10 \mathrm{~kg} / \mathrm{s}\), and ejects gas at atmospheric pressure with a speed of \(2500 \mathrm{~m} / \mathrm{s}\) relative to the rocket? What would be the maximum velocity? Plot the rocket speed as a function of time for the first minute of flight.