Question

When sound is produced in an aeroplane moving with a velocity of $200 \,m/s$ horizontal its echo is heard after $10\sqrt{5}\,s.$ If velocity of sound in air is the elevation of aircraft is

• A. $250 \,m$
• B. $250\sqrt{5}\,m$
• C. $12.50\,m$
• D. $2500\, m$

Answer 1

Answer: (D)

$2500\, m$

Answer 2

From the figure for sound travel $ABC$
Given,

Time for the echo $=10\, \sqrt{5}$ s
Velocity of the plane $=200\, m / s$
Here, $O C=200 \times 5 \sqrt{5}=2236\, m$
$B C=$ velocity of sound $\times 5 \sqrt{5}$
$\Rightarrow B C=300 \times 5 \sqrt{5}=3354\, m$
$\therefore O B=\sqrt{B C^{2}-O C^{2}}$
$O B=2500\, m$