Q 11-03-165JEE MainJEE Main 2019 (12 Jan, Shift 1)Medium
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:
Answer: (C) $\dfrac v2$
The sound heard now was emitted from a point P where the line to the person makes $60^\circ$ with the ground. In the time $t$ the sound travels from P to the person (distance $vt$), the plane flies horizontally from P to the point overhead.
The horizontal distance from P to the overhead point is $vt\cos60^\circ$, so
$$v_{\text{plane}}\,t = vt\cos60^\circ \Rightarrow v_{\text{plane}} = \frac v2$$
Solution by Sreeraj P, M.Sc Physics