A rocket has an initial mass of 25,000 kg of which 20,000 kg is fuel and oxygen. It is propelled directly upward from ground level (initial velocity V0 = 0) by a rocket engine with a constant thrust of 400,000 N created by 1000kg/s of combustion products exiting the rocket nozzle at a constant velocity of 400 m/s. The combustion products are created solely by the fuel and oxygen onboard the rocket. What is the time to burnout (all onboard fuel and oxygen exhausted)? Plot thrust vs. time. What is the velocity of the rocket at 15, 20 and 30 seconds? Find the maximum altitude attained by the rocket. Ignore air friction.
A force balance on the rocket yields the ordinary differential equation
m(t)dVdt- b vd = -m(t)g , m(t) = m0 - b*t
where b = fuel/oxygen burn rate in kg/s, m0 = initial total rocket mass in kg, vd is the exit velocity of the burning fuel/oxygen mixture in m/s (thrust = b * vd in N), and g is the acceleration of gravity.