# A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle 60o with groung level. But he finds the aeroplane right vertically above his position. If v is the speed of sound, speed of the plane is :Option 1)vOption 2)$\frac{\sqrt{3}}{2} v$Option 3)$\frac{2v}{\sqrt{3}}$Option 4)$\frac{v}{2}$

Relative Velocity -

Relative velocity of a body, A with respected body B when the to bodies moving at an angle $\Theta$.

$V_{AB}= \sqrt{V_{A}^{2}+V_{B}^{2}+2V_{A}V_{B}\cos \left ( 180-\theta \right )}$

$= \sqrt{V_{A}^{2}+V_{B}^{2}-2V_{A}V_{B}\cos \left ( \theta \right )}$

- wherein

$\\*V_{A}= velocity\: of\: A\\* V_{B}= velocity\: of\: B\\* \Theta = angle \: between \: A \: and \: B$

time= $\frac{d}{V_{s}}=\frac{AB}{V_{p}}$

$AB= d\, Cos60$

So $V_{p}=V_{s}\times \frac{dCos60}{d}$

$V_{p}=V_{s}\, \, Cos60$

$V_{p}=\frac{V_{s}}{2}=\frac{V}{2}$

Option 1)

v

Option 2)

$\frac{\sqrt{3}}{2} v$

Option 3)

$\frac{2v}{\sqrt{3}}$

Option 4)

$\frac{v}{2}$

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