Final answer:
According to Newton's third law, the cannon recoils modestly when firing a cannonball because of its much larger mass, while the cannonball flies off at high speed. Momentum is conserved, explaining the different velocities. The recoil velocity of the cannon is significantly lower than the velocity of the cannonball.
Step-by-step explanation:
The inquiry refers to Newton's third law of motion, which states for every action there is an equal and opposite reaction. Applying this law to a cannon and a cannonball, they exert equal forces on each other, but the consequences of these forces are not the same due to different masses. When a cannon fires a cannonball, by Newton's third law, the cannon experiences a backward force equal in magnitude to the forward force on the cannonball. However, due to the cannon's significantly larger mass compared to the cannonball, its acceleration is much smaller, leading to a modest recoil velocity.
Let's analyze the situation using momentum conservation and kinetic energy. The total momentum of the system before firing is zero since both the cannon and the cannonball are stationary. After firing, the cannonball acquires a high velocity due to its relatively low mass. In contrast, the cannon recoils with a lower velocity because it has a much greater mass.
As for the vertical component of the cannonball's momentum, it is transferred to the Earth when the cannon recoils, and since the Earth's mass is vast, it essentially remains stationary. The kinetic energy of the cannon dissipates as heat in shock absorbers, stopping its recoil.