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Root Mean Square Speed

A horizontal ...

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}

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B

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

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C

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

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D

\frac{2 v}{a}

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Solution

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 $V_{r e l}$ be the velocity of wind w.r.t man:
$V_{m} = a t, V_{r} = \sqrt{V^{2} - V_{m}^{2}}$
when $V_{m} = V_{r},_{r}$ will be along east.
$a t = \sqrt{V^{2} - a^{2} t^{2}}$
$a^{2} t^{2} = V^{2} - a^{2} t^{2}$
$V^{2} = 2 a^{2} t^{2}$
$t = \frac{V}{\sqrt{2} a}$

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