According to basic mechanics, why does a cannon recoil backward after firing a projectile from its barrel?

Introduction / Context:
Recoil of firearms and cannons is a classic example used to illustrate basic laws of motion. When a shell is fired forward, the cannon moves backward. Understanding this effect helps students grasp Newton third law and conservation of momentum in practical situations. This question asks which principle best explains why the cannon recoils when the projectile is launched.

Given Data / Assumptions:

• A cannon and a projectile initially rest together before firing.
• On firing, the projectile is propelled forward at high speed.
• The cannon is free to move backward on its mount or platform.
• External horizontal forces such as friction are neglected during the brief firing interval.
• Newton laws of motion apply to the system.

Concept / Approach:
Newton third law of motion states that for every action there is an equal and opposite reaction. When the expanding gases exert a forward force on the projectile, the projectile exerts an equal and opposite force on the cannon. In addition, conservation of linear momentum tells us that the total momentum of the isolated cannon projectile system remains zero, so if the projectile gains forward momentum, the cannon must gain backward momentum. Both ideas imply that the cannon moves backward in response to the forward motion of the projectile.

Step-by-Step Solution:
Step 1: Initially, the cannon and projectile system is at rest, so total momentum is zero.Step 2: When the gunpowder burns, expanding gases push the projectile forward, giving it a large forward momentum.Step 3: According to Newton third law, the projectile exerts an equal and opposite force on the cannon, pushing it backward.Step 4: As a result, the cannon acquires backward momentum such that the total momentum of the system remains conserved and equal to zero.

Verification / Alternative check:
Experiments with small air rifles or toy guns show the same effect: when a projectile is fired forward, the gun jerks backward. Mathematical treatment using conservation of momentum matches observed recoil speeds, confirming that momentum, not energy alone, must be considered. Newton third law explains the force pair involved, while conservation of momentum explains the subsequent motion. Gravitational forces do not change suddenly during firing and cannot account for the recoil.

Why Other Options Are Wrong:
Option a is wrong because conservation of energy alone does not dictate the direction of motion; energy is scalar and cannot explain equal and opposite recoils directly. Option b is incomplete; although hot gases push on both projectile and cannon, it is the mutual interaction described by Newton third law that correctly explains the recoil and is usually cited in basic physics. Option d is incorrect because Newton first law deals with inertia and tendency to remain at rest or in uniform motion, not with action reaction pairs. Option e is clearly wrong since gravity acts mostly vertically in this context and does not suddenly pull the cannon backward when firing.

Common Pitfalls:
Students sometimes focus only on the gases pushing on the projectile and forget that forces come in pairs. Another confusion is to overuse the term conservation of energy without recognising that direction and vector quantities are crucial for describing recoil. It is helpful to remember that when two bodies interact, such as a cannon and shell, the forces they exert on each other are equal and opposite, which is exactly Newton third law. Combined with momentum conservation, this law gives a complete explanation of recoil phenomena.

Final Answer:
Because of Newton third law of motion, which relates action and reaction forces.