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.