Question

how does conservation of momentum takes place in
1.a rocket taking off from ground
2.flying of a jet aeroplane

Answer 1

In the first case,
In a rocket, the hot gases produced by the rapid burning of fuel rush out of a jet at the bottom of the rocket at a very high speed.The equal and opposite reaction force of the downward going gases pushes the rocket in the upward direction with a great speed.
In the second case,
In the modern jet aircraft, the hot gases obtained by the rapid burning of the fuel rush out of a jet (a nozzle) at the rear end (back end) of the aircraft at a great speed. The equal and opposite reaction force of the backward going gases pushes the aircraft forward at a great speed.

Answer 2

There are two laws. One is the law of conservation of linear momentum and another is the law of conservation of angular momentum about the axis of revolution. 1. When the external force on a system of bodies is zero, then the total linear momentum of the system of bodies remains constant (in time and space). 2. When the external torque acting on a system of bodies is zero, then the angular momentum of the system of bodies is a constant (over the period of time and in space). 1) A rocket taking off from ground The hot burning gases coming out of the exhaust at very high pressure from behind, and the rest of the jet are the two bodies. Before the hot gases are ejected, the total linear momentum is zero (stationary). The total instantaneous momentum of both is conserved. The rate of change in the momentum of hot gases downward direction, is equal to the rate of change in momentum of the rest of rocket in vertically upward direction. So it takes off at very high acceleration, due to the thrust. 2) Flying of a jet airplane in space/sky There are forces like drag of air, a lift from air from below airplane and the weight of airplane. These are balanced partially by a little inclination of the aircraft to the direction of velocity. Conservation of momentum principle is applied, as in the above description, to the fuel and rest of jet. The rates of burning and ejection of exhaust gases in the fuel burning chamber are adjusted to get the desired increase in the momentum (or desired thrust) in the forward direction.