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  • Help me solve this 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

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)

    v

  • Option 2)

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

  • Option 3)

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

  • Option 4)

    \frac{v}{2}

Answers (1)

best_answer

 

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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