question_answer

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

Correct Answer: D

Solution :

                 From the figure for sound travel ABC Given, Time for the echo \[=10\sqrt{5}s\] Velocity of the plane = 200 m/s Here, \[OC=200\times 5\sqrt{5}=2236\,m\] BC = velocity of sound \[\times \,\,5\sqrt{5}\] \[\Rightarrow \]\[BC=300\times 5\sqrt{5}=3354\,m\] \[\therefore \]  \[OB=300\times 5\sqrt{5}=3354\,m\]                 \[OB=2500\,\,m\] The plane is 2500 m above the ground.