Question

A horizontal wind is blowing with a velocity $v$ towards north-east. A man starts running towards north with acceleration $a$. The time after which man will feel the wind blowing towards east is

• A. $\frac{v}{a}$
• B. $\frac{\sqrt{2}v}{a}$
• C. $\frac{v}{\sqrt{2}a}$
• D. $\frac{2v}{a}$

Answer 1

The correct option is C $\frac{v}{\sqrt{2}a}$



Velocity of wind ${\overrightarrow{v}}_w=\frac{v}{\sqrt{2}}\hat{i}+\frac{v}{\sqrt{2}}\hat{j}{\overrightarrow{v}}_m=\left(at\right)\hat{j}{\overrightarrow{v}}_{wm}={\overrightarrow{v}}_w-{\overrightarrow{v}}_m=\frac{v}{\sqrt{2}}\hat{i}+(\frac{v}{\sqrt{2}}-at)\hat{j}$
It appears due east when,
$\frac{v}{\sqrt{2}}-at=0$
$\therefore t=\frac{v}{\sqrt{2}a}$