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 ?

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 

Best Of luck

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