Question

At t=0, an aeroplane which is vertically above a ground observer is going towards east at a speed of $510km/h$ at a height of $2000m$. At a certain instant, the sound of the plane heard by the ground observer appears to come from a point vertically above him. How far is the plane at this instant from where it was at t=0? Speed of the sound in air $=340m/s$.

• A. $633m$
• B. $733m$
• C. $833m$
• D. $933m$
  

Answer 1

The correct option is C $833m$



The sound reaching the ground observer P, was emitted by the plane when it was at the point Q vertically above his head. The time taken by the sound to reach the observer is
$t=\frac{2000m}{340m/s}=\frac{100}{17}s$
The distance moved by the plane during this period is
$d=\left(510km/h\right)\left[\frac{100}{17}s\right]$
$=\frac{30\times {10}^5}{3600}m=833.33m$.

Thus the plane will be 833 m ahead of the observer on its line of motion when he hears the sound coming vertical to him.