Question

A person moves $20\text{m}$ towards north-east and then moves $20\text{m}$ towards west and then again moves $20\text{m}$ towards north-east and stops. The magnitude of displacement of the person is :

• A. $20\sqrt{5-2\sqrt{2}}\text{m}$
• B. $20\text{m}$
• C. $20\sqrt{5+2\sqrt{2}}\text{m}$
• D. None of these

Answer 1

The correct option is A $20\sqrt{5-2\sqrt{2}}\text{m}$


Net displacement $\overrightarrow{S}=\overrightarrow{S_1}+\overrightarrow{S_2}+\overrightarrow{S_3}$
$=(20\cos {45}^{\circ }\hat{i}+20\sin {45}^{\circ }\hat{j})+(-20\hat{i})+(20\cos {45}^{\circ }\hat{i}+20\sin {45}^{\circ }\hat{j})$
$=20(\sqrt{2}-1)\hat{i}+20\sqrt{2}\hat{j}$

$\therefore |\overrightarrow{S}|=\sqrt{{\left[20\right(\sqrt{2}-1\left)\right]}^2+(20\sqrt{2}{)}^2}$
$=20\sqrt{5-2\sqrt{2}}\text{m}$