Question

A person moves $30m$ north and then $20m$ towards east and finally $30\sqrt{2}m$ in south-west direction. The displacement of the person from the origin will be

• A. $10m$along north
• B. $10m$ long south
• C. $10m$along west
• D. $Zero$

Answer 1

The correct option is C $10m$along west

From figure, $\overrightarrow{OA}=0\overrightarrow{i}+30\overrightarrow{j},\overrightarrow{AB}=20\overrightarrow{i}+0\overrightarrow{j}$

$BC=-30\sqrt{2}cos{45}^{\circ }\overrightarrow{i}-30\sqrt{2}sin{45}^{\circ }\overrightarrow{j}=-30\overrightarrow{i}-30\overrightarrow{j}$
$\therefore$ Net displacement, $\overrightarrow{OC}=\overrightarrow{OA}+\overrightarrow{AB}+\overrightarrow{BC}=-10\overrightarrow{i}+0\overrightarrow{j}$
$|\overrightarrow{OC}|=10m$
From figure we can tell that the direction is towards west.