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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 getv = x (1/t1 + 1/t2) / 2on subtracting,u = x (1/t1 - 1/t2) / 2in the second case,the resultant velocity and u are at 900 to each othertherefore,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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