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
2√3v
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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.