Question

A person has to go $50m$ due south, $40m$ due west and $20m$ due north to reach his destination. The displacement of the person is

• A. 50 m
• B. 100 m
• C. 500 m
• D. 0

Answer 1

Answer: (A)

50 m

On considering East as positive x-axis and North as positive y-axis.

Given A person move 5030 meters south $(-50\hat{j})$, then 4020 meters west$(-40\hat{i})$,then 20302 meters north $\left(20\hat{j}\right)$.

So, the displacement is the sum of three $=-50\hat{j}-40\hat{i}+20\hat{j}=-(40\hat{i}+30\hat{j})$

Therefore, his final displacement from its original position $=\sqrt{{30}^2+{40}^2}=50m$