The Third Law of Motion, formulated by Sir Isaac Newton, states that for every action, there is an equal and opposite reaction. This principle is fundamental in understanding the interactions between objects.

In simple terms, if an object A exerts a force on object B, then object B exerts a force of equal magnitude and opposite direction on object A. Mathematically, this can be expressed as:

If $F_{AB}$ is the force exerted by A on B and $F_{BA}$ is the force exerted by B on A, then:

$F_{AB} = -F_{BA}$

This law can be observed in various everyday scenarios. For example, when you jump off a small boat onto the shore, you push the boat backward as you propel yourself forward. The action is your jump, and the reaction is the boat moving in the opposite direction.

Another classic example is the propulsion of rockets. When a rocket engine expels gas downwards, the reaction force pushes the rocket upwards. This can be illustrated with the equation:

Thrust = $-\Delta p / \Delta t$

Where $\Delta p$ is the change in momentum and $\Delta t$ is the change in time.

The Third Law of Motion is crucial for understanding motion in a variety of physical systems. It emphasizes that forces always occur in pairs, known as action-reaction pairs. These pairs are equal in size but opposite in direction.

In sports, this law can be observed in activities such as swimming or running. When a swimmer pushes the water backward with their hands, the water pushes the swimmer forward, allowing them to move through the water effectively.

Similarly, when a football player kicks a ball, the force exerted on the ball by the player's foot is met with an equal and opposite force exerted by the ball on the foot. This interaction allows the ball to travel in the desired direction.

It's important to note that the forces in action-reaction pairs act on different objects. This means they do not cancel each other out because they do not act on the same body. Understanding this concept is essential for analyzing the dynamics of systems in physics.

Applications of the Third Law of Motion can be seen in various engineering and technology fields. For instance, the design of vehicles, aircraft, and even amusement park rides take into account the interactions described by this law to ensure stability and functionality.