Question
Sun March 22, 2015 By: R K Jha

Find the distance of cloud from you when you hear a thunder 3 seconds after the lightning is seen. Given speed of light =3x108 m/sec, speed of sound = 330m/sec. Also draw the figure.

Expert Reply
Yashvanti Jain
Mon March 23, 2015
We know that the speed of light is greater than the speed of sound. Thus, lightning will reach in no time but the thunder will be heard 3 seconds after the lightning by the man.
We know that the lightning and the sound travels the same distance, let us consider that as 'd'.
Let 'v1' and 't1' be the velocity of the lightning and the time taken by it to reach the man. Similarly, 'v2' and 't2' be the velocity and the time taken by the thunder to reach the man.
begin mathsize 12px style straight d space equals space straight v subscript 1 space straight t subscript 1 space equals space space straight v subscript 2 space straight t subscript 2 space straight v subscript 1 space straight t subscript 1 space equals space space straight v subscript 2 space left parenthesis straight t subscript 1 space plus space 3 right parenthesis Or comma space straight t subscript 1 space equals space fraction numerator 3 straight v subscript 2 over denominator straight v subscript 1 minus space straight v subscript 2 end fraction space equals space space fraction numerator 3 space cross times space 330 over denominator 3 space cross times space 10 to the power of 8 minus space 330 end fraction space equals space 3.30 space cross times 10 to the power of negative 6 end exponent space straight s rightwards arrow Distance comma space straight d equals space space straight v subscript 1 space straight t subscript 1 space equals space space 3 cross times space 10 to the power of 8 space cross times space 3.30 space cross times 10 to the power of negative 6 end exponent space equals space 990 space straight m end style 
Thus, the cloud is at a distance of 990 m from the man.
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