Let m₀ be the mass of the rocket at time t = 0. m its mass at any time t and v its speed a that the velocity of the rocket is u.

Further, let (-dm/dt) be the mass of the gas removed per unit time and v_r the exhaust velocity of the gases. Generally (-dm/dt) and v_r are kept constant throughout the journey of the rocket. Now, let us take few equations which can be needed in the problems of rocket propulsion. At time t = t,

1.         Thrust force on the rocket

                        F_t=v_r(-dm/dt)                                                               (upwards)

2.         Weight of the rocket

                        W = mg                                                                       (downwards)

3.         New force on the rocket

                        F_net = F_t - W                                                                 (upwards)

            Or        F_net=v_r(-dm/dt)-mg

4.         Net acceleration of the rocket a=F/m

            Or        dv/dt = v_r/m(-dm/dt)-g           Or        dv = v_r(-dm/dt)-gdt

            Or                   Or        v-u=v_r ln(m₀/m)-gt

Thus,                v = u-gt + v_r ln(m₀/m)                                     ... (i)

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