Question

A person move $30$ meters north, then $20$ meters east,then $30\sqrt{2}$ meters south-west. His displacement from the original position is:

• A. 100 m west
• B. 10 m west
• C. 10 m East
• D. 10 m North

Answer 1

The correct option is B 10 m west

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

Given A person move 3030 meters north$\left(30\hat{j}\right)$, then 2020 meters east$\left(20\hat{i}\right)$,then 30√2302 meters south-west$\left[30\sqrt{2}\right(\frac{-\hat{i}-\hat{j}}{\sqrt{2}}\left)\right]$.

So, the displace ment is the sum of three $=20\hat{i}+30\hat{j}+30\sqrt{2}\left(\frac{-\hat{i}-\hat{j}}{\sqrt{2}}\right)$

$=-10\hat{i}$

Therefore, his final displacement from its original position is $10m$ west.