State and prove the law of conservation of linear momentum. Explain rocket propulsion using it.

1. 1 · State the law in one line. The total linear momentum of a system stays constant when no net external force acts on it.
2. 2 · Draw the collision. [Diagram: two balls m₁ and m₂ before, during and after collision, with u₁, u₂, F₁, F₂, v₁, v₂ marked]
3. 3 · Write the two forces.
   • Force on m₂ (action): F₂ = m₂(v₂ − u₂)/t
   • Force on m₁ (reaction): F₁ = m₁(v₁ − u₁)/t
4. 4 · Use the third law. F₁ = −F₂, so m₁(v₁ − u₁) = −m₂(v₂ − u₂). Rearranging: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂.
5. 5 · Explain rocket propulsion.
   • Burning fuel sends hot gases backward through the nozzle.
   • The rocket gains an equal forward momentum.
   • Its mass falls as fuel burns, so its velocity rises, up to the escape velocity of 11.2 km s⁻¹.
6. 6 · Real-life link. Gun recoil, a balloon rushing forward as air escapes, rockets launched from Sriharikota.
7. 7 · Close in one line. Momentum before a collision equals momentum after it, and this is why rockets can fly even in space.

Scoring tip: The derivation carries most of the marks. Write it neatly with subscripts and say clearly where you used the third law.