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When sound is produced in an aeroplane w...

When sound is produced in an aeroplane with a velocity of 200 m/s horizontally its echo is heard after `10sqrt(5)` seconds. If velocity of sound in air is 300 `ms^(-1)` the elevation of aircraft is

A

250 m

B

`250 sqrt(5)` m

C

1250 m

D

2500 m

Text Solution

Verified by Experts

The correct Answer is:
D
Time for the echo `=10sqrt(5)s` (i.e. For sound to travel ABC)
Velocity of the plane = 200 m/s
OC `=200 xx 5sqrt(5) = 2236`m
BC = velocity of sound ` xx 5sqrt(5)`
`rArr` BC `=300 xx 5sqrt(5) = 3354`m
`therefore OB = sqrt(BC^(2) - OC^(2))`
`rArr OB ~= 2500 m` The plane is 2500 m abvoe the ground.
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