Chapter 3, Problem 18Q

Solution

To Determine:

The reason for the other train to appear to be moving backwards if one is riding on a train that speeds past another train moving in the same direction on an adjacent track.

Solution: This happens because the observeris at rest in his frame of reference. The observer can’t understand his own motion. When an observer in train A is at rest in his frame of reference,the train appearsto be going in opposite direction.

Explanation:

  ${\overrightarrow{v}}_{BA}=$ Velocity of train B with respect to A

  ${\overrightarrow{v}}_B\text{=}$ Velocity of train B

  ${\overrightarrow{v}}_A\text{=}$ Velocity of train A Let train A be moving with velocity $v_A$ rightward, which overtakes another train B moving in the same direction with velocity $v_B$ .

  $\left(v_B<v_A\right)$

According to the question:

  $\begin{array}{l}{\overrightarrow{v}}_{BA}={\overrightarrow{v}}_B-{\overrightarrow{v}}_A\\ =\text{Negative value}\end{array}$

It means that train B appears to move leftward by an observer who is in train A.

Conclusion:

If one is riding on a train that speeds past another train moving in the same direction on an adjacent track, it appears as moving backward because observer can’t feel his own motion, the person always assumesto be at rest in his or her frame of reference.ss