Classical mechanics — recoil of a gun Which law of motion explains the recoil of a gun when a bullet is fired (the gun moves backward as the bullet moves forward)?

Introduction / Context:
The recoil of a gun is a classic illustration used in physics to demonstrate action–reaction behavior. When a projectile is expelled at high speed, the gun experiences a backward motion. Identifying the correct Newtonian principle behind this phenomenon is a foundational skill for mechanics and engineering students.

Given Data / Assumptions:

• A gun fires a bullet forward with high momentum.
• The gun and bullet form an isolated system for a very short interval.
• External horizontal forces during the impulse are negligible.

Concept / Approach:
Newton's third law states that for every action there is an equal and opposite reaction. Simultaneously, conservation of linear momentum applies to an isolated system: m_bullet * v_bullet + m_gun * v_gun = constant (typically zero before firing). The equal and opposite interaction forces during the short firing interval generate impulses that change the momenta of both bodies in opposite directions.

Step-by-Step Solution:

Verification / Alternative check:
Using momentum conservation: m_bullet * v_bullet + m_gun * v_gun = 0 (initially at rest). Thus v_gun = − (m_bullet / m_gun) * v_bullet, confirming backward motion with smaller speed due to higher gun mass.

Why Other Options Are Wrong:

• First law: Inertia alone does not cause recoil.
• Second law: Relates force to acceleration but does not explain equal and opposite impulses here.
• None of these / energy only: Energy conversion occurs, but recoil specifically demonstrates action–reaction.

Common Pitfalls:
Attributing recoil solely to gas escape or energy without recognizing the paired interaction forces and momentum balance.

Final Answer:
Newton's third law of motion