question_answer

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

A) 250 m                                   

B) 250\[\sqrt{5}\] m

C) 1250 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 \[\times 5\sqrt{5}\] \[\Rightarrow \]\[BC=300\times 5\sqrt{5}=3354\,m\] \[\therefore \]   \[OB=\sqrt{B{{C}^{2}}-O{{C}^{2}}}\] \[OB=2500\,m\] The plane is 2500 m above the ground.