A rocket works on conservation of momentum. The expelled gases from the engine propel the rocket upward. The thrust is given by

F = v_o(dm/dt)

where v_o is the exhaust gas speed and dm/dt is the burn rate (r). The burn time t_b is given by

t_b = M_F/r

where M_F is the mass of the fuel. The velocity at burnout (v_b) is given by

v_b = v_oLn(R) - gt_b

where M = (M_F + M_o)/M₀ and M_o is the Mass of the empty rocket.

Its height at burnout (y_b) is

y_b = v_ot_b - (1/2)gt_b² + M_orLn(R)/r

After burn out it achieves a final height of

y = y_b + v_b²/2g.


In the movie at the left you can specify the parameters r, v_o and M_F. Launch the rocket by clicking on it. In general, you want to get the most height for the least amount of fuel. The simulation assumes constant g (it would vary by 15% over 500 km) and no air resistance. The first would increase the height; the second would decrease it.