Question

When sound is produced in an aeroplane moving with a velocity of $200m/s$ horizontal its echo is heard after $10\sqrt{5}s$. If velocity of sound in air is $300m/s$, the elevation of aircraft is

• A. $250m$
• B. $250\sqrt{5}m$
• C. $1250m$
• D. $2500m$

Answer 1

The correct option is D $2500m$

Horizontal distance moved in $5\sqrt{5}$ s, $AD=200\times 5\sqrt{5}=1000\sqrt{5}$ m

Distance covered by sound in air in that period $AC=300\times \sqrt{5}=1500\sqrt{5}$ m

Elevation of aircraft $h=\sqrt{(1500\sqrt{5}{)}^2-(1000\sqrt{5}{)}^2}$

$\therefore$ $h=100\sqrt{5}\left(\sqrt{(15{)}^2-(10{)}^2}\right)$

$⟹$ $h=100\sqrt{5}\times 5\sqrt{5}=2500$ m