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Question

A person standing on open ground hears the sound of a jet airplane, coming from the north at an angle 30 with the horizontal. But he finds the airplane vertically above his position. If v is the speed of sound, then speed of the plane is

A
32v
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B
v
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C
23v
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D
v2
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Solution

The correct option is A 32v
Let the height of airplane be d from the ground.


As sound produced by the airplane at point A reaches the man at point O, the airplane moves to point B and will be vertically above the man.
Time taken by sound to reach the man
t=dv
t=dvsin30 ...(1)
In the same time, the airplane will go from point A to B, hence speed of the airplane is,
v0=ABt


Substituting from the triangle shown and Eq.(1),
v0=(dtan30)(dvsin30)
v0=3v2
The speed of the plane is 3v2.

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