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 $\frac{v}{\sqrt{2}a}$

Let V be the velocity of wind $V_m$ be the velocity of man and $V_{rel}$ be the velocity of wind w.r.t man:

$V_m=at,V_r=\sqrt{V^2-V_m^2}$

when $V_m=V_r,\overrightarrow{V_r}$ will be along east.

$at=\sqrt{V^2-a^2{t}^2}$

$a^2{t}^2=V^2-a^2{t}^2$

$V^2=2a^2{t}^2$

$t=\frac{V}{\sqrt{2}a}$