11.1 Relative Motion

11.1 Relative Motion

Consider throwing a ball to your right. For someone facing you, this direction appears to his left. This illustrates that direction is a relative concept. Similarly, the state of rest or motion of an object depends on the observer. For example, the walls of a moving train seem stationary to passengers inside the train but appear to be moving to someone standing on the ground. Thus, we cannot definitively say whether an object is absolutely at rest or in motion; all motions are relative to the observer or to the reference frame being used. This becomes evident with the following example: An observer in a closed train compartment uses the compartment as his frame of reference. To determine the train's motion, the observer drops a ball and measures the horizontal distance travelled by the ball, keeping the vertical distance the same in each case. It is assumed that the vertical distance is covered in "$t$" seconds in all scenarios.

Case (a): Suppose the train is stationary. In that case, the horizontal velocity of the ball will be zero, and the horizontal distance travelled will also be zero. In this scenario, the observer's view inside the train and by some means outside the train will be identical. The ball will have fallen to a point on the floor directly below the point from where it was dropped (Fig. 11.1-a).

Case (b): The train is moving with a uniform velocity $v_{0}$. When the ball is released, it has an initial horizontal velocity $v_{x}$ and behaves like a projectile. It travels a horizontal distance $x$ in time $t$ it takes for the ball to reach the floor. Since both the train and the observer inside it are moving with the same velocity $v_{0}$, they both travel the same horizontal distance $x$ in the same time $t$, therefore, the observer inside the train sees that the ball falls to a point on the floor directly below where it was dropped. In contrast, an observer outside the train will see the ball following a projectile path, as shown in Fig. 11.1(b). Thus, observers in different frames of reference, moving with uniform velocity relative to each other, will perceive motion differently.