Question

A student sees a jet plane flying from east to west. When the jet is seen just above his head the sound of Jet appears to reach him making ${60}^{\circ }$ with the horizontal from east. If the velocity of sound is $C$, then that of the jet plane is :

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

Answer 1

Answer: (B)

$\frac{C}{2}$

According to the problem, $\angle ABC={60}^{\circ }$

Time taken by plane to travel AB is same as time taken by sound to travel BC.

Thus $AB=vt$

$BC=ct$

From geometry,

$\frac{AB}{BC}=\frac{v}{c}=cos{60}^{\circ }=\frac{1}{2}$

$⟹v=\frac{c}{2}$