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.