# two friends A and B are standing at a distance x apart in an open field and wind is blowing from A to B. A beats the drum and B hears the sound. suppose A and B shift their position in such a way that the line joining them becomes perpendicular to the direction of the wind while maintaining the distance x. what will be the time lag  B finds between seeing and hearing the drum beating by A ?

Aman Bansal
592 Points
12 years ago

Dear Student,

the velocity of sound and wind are added vectorially.
therefore, in the first case,

v + u = x/t1 ........................ (1)

v - u = x/t2 ...........................(2)
on adding, we get
v = x (1/t1 + 1/t2) /  2
on subtracting,
u = x (1/t1 - 1/t2) /  2

in the second case,

the resultant velocity and u are at 900 to each other
therefore,if u make a rt. triangle,

v acts as hypotenuse and u as a leg and resultant vel. towards B makes the other leg. therefore,
Resultant vel. =   v2 - u2
time taken =     x
v2 - u2

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Aman Bansal