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Question

At t=0, an aeroplane which is vertically above a ground observer is going towards east at a speed of 510 km/h at a height of 2000 m. At a certain instant, the sound of the plane heard by the ground observer appears to come from a point vertically above him. How far is the plane at this instant from where it was at t=0? Speed of the sound in air =340 m/s.

A
633m
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B
733m
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C
833m
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D
933m
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Solution

The correct option is C 833m


The sound reaching the ground observer P, was emitted by the plane when it was at the point Q vertically above his head. The time taken by the sound to reach the observer is
t=2000 m340 m/s=10017 s
The distance moved by the plane during this period is
d=(510 km/h)[10017 s]
=30×1053600m=833.33m.

Thus the plane will be 833 m ahead of the observer on its line of motion when he hears the sound coming vertical to him.

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