Question

A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle ${60}^{\circ }$ with ground level. But he finds the aeroplane right vertically above his position. If $v$ is the speed of sound, speed of the plane is :

• A. $\frac{v}{2}$
• B. $\frac{\sqrt{3}}{2}v$
• C. $v$
• D. $\frac{2v}{\sqrt{3}}$

Answer 1

The correct option is A $\frac{v}{2}$


Distance, $PQ=v_p\times t(\text{Distance = speed}\times \text{time})$

Distance, $QR=v.t$

$\cos {60}^{\circ }=\frac{PQ}{QR}$

$\frac{1}{2}=\frac{v_p\times t}{v.t}\Rightarrow v_p=\frac{v}{2}$