Law Of Conservation Of Momentum

The momentum of an isolated system remains constant ;

 ;total momentum of a system before collision is equal to total momentum after collision.

Let the mass of a rocket is m1 and mass of fuel is m2. Before the rocket ignition, momentum of rocket and fuel is zero because both are at rest , so total momentum is also zero. After ignition the direction of movement of the rocket is opposite to the exhaust gasses and in this case both have momentum with opposite signs.After ; the sum of total momentum is also zero. Let after ignition the velocity of rocket is "u" and exhaust gasses "v". ;

The momentum of rocket = m1u

The momentum of exhaust gasses=m2v

Total momentum= m1u+m2v

According to law of conservation of momentum ;

Total momentum before collision=total momentum after collision ;

0=m1u+m2v, m1u=-m2v

So u=-m2v/m1

With the passage of time mass of rocket m1 will decrease due to exhausted gasses and hence velocity of rocket ; will increase.