Question

A train is moving towards the east with a speed 20 m/s. The person is running on the roof of the train with a speed 3 m/s against the motion of the train. Velocity of the person as seen by an observer on ground will be:
A. 23 m/s towards East
B. 17 m/s towards East
C. 23 m/s towards West
D. 17 m/s towards West

Answer 1

Hint: Specify the positive and negative direction of motion of the train and person running over the roof. Use the relative velocity concept to express the speed of a person running over the roof of a train.

Complete step by step answer:We assume the direction towards East is positive and the direction towards West is negative. We can show the direction of motion of the train and person running over the roof as shown in the figure below.

In the above figure, the direction of movement of a person running over the roof of the train is towards the west and the direction of motion of the train is towards the east.

We can express the velocity of the person as seen by the observer on the ground as follows,
\[\vec v = {v_{train}}\hat i + {v_{person}}\left( { - \hat i} \right)\]
\[\vec v = {v_{train}}\hat i - {v_{person}}\hat i\]

Substitute 20 m/s for \[{v_{train}}\] and 3 m/s for \[{v_{person}}\] in the above equation.
\[\vec v = 20\hat i - 3\hat i\]
\[ \Rightarrow \vec v = 17\hat i\]

Since the unit vector \[\hat i\] represents direction towards east, we observe the velocity of person as seen by the observer towards east. Therefore, we can see that the velocity of the person running over the roof of the train is 17 m/s towards East as seen by the observer on the ground.

So, the correct answer is option (B).

Note:To solve such questions, represent the directions by \[\hat i\] and \[\hat j\]. Therefore, the Eastward direction is \[\hat i\] and Westward is \[ - \hat i\]. The Northward direction is \[\hat j\] and Southward direction is \[ - \hat j\]. If the velocity is towards South-East or North-East, the velocity has both \[\hat i\] and \[\hat j\] components.