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Question

A bullet is fired and it hits a target. An observer in the same plane heard two sounds: the crack of the rifle and the thud of the bullet striking the target at the same instant. Then the locus of the observer is a

A
Ellipse
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B
Hyperbola
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C
Parabola
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D
Circle
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Solution

The correct option is B Hyperbola
Let the target at B and fire point A
let the coordinate of the observer is P
If velocity of sound is vs
Time required to reach the sound of crack to the observer t1 and time required to reach the sound of the thud is t2(t1>t2)
Then PB=vst2
PA=vst1PAPB=t1t2>1
So the path will be hyperbola


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