Q. An aeroplane be is above the head of an observer and the sound appears to be coming at an angle of $60^{0}$ with the vertical. If velocity of sound is $v$, then the speed of aeroplane is
A) $v$
B) $\frac{\sqrt{3}}{2}v$
C) $\frac{v}{2}$
D) $2$
Explanation
(b) When aeroplane is at $P_{2}$ vertically above the observer O, sound comes along $P_{1}O$ at $60{^\circ}$ with the vertical.
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$\therefore P_{1}O = v \times t,P_{1}P_{2} = v_{p}t$.
$\sin{60{^\circ} = \frac{P_{1}P_{2}}{P_{1}O}} = \frac{v_{p}t}{v \times t} = \frac{v_{p}}{v}$
$\therefore v_{p} = v\sin{60{^\circ} = v\sqrt{3}/2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.