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Standard XII

Physics

Relative Velocity in 2D

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

\frac{v}{a}

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

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

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\frac{2 v}{a}

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Solution

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

Velocity of wind ${\to v}_{w} = \frac{v}{\sqrt{2}}^i + \frac{v}{\sqrt{2}}^j {\to v}_{m} = (a t)^j {\to v}_{w m} = {\to v}_{w} - {\to v}_{m} = \frac{v}{\sqrt{2}}^i + (\frac{v}{\sqrt{2}} - a t)^j$
It appears due east when,
$\frac{v}{\sqrt{2}} - a t = 0$
$∴ t = \frac{v}{\sqrt{2} a}$

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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

The correct option is C v√2a Velocity of wind →vw=v√2^i+v√2^j→vm=(at)^j→vwm=→vw−→vm=v√2^i+(v√2−at)^j It appears due east when, v√2−at=0 ∴t=v√2a

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