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Suppose A and B in the previous problem

Question:

Suppose A and B in the previous problem change their positions in such a way that the line joining them becomes perpendicular to the direction of wind while maintaining the separation $x$. What will be the time lad $B$ finds between seeing and hearing the drum beating by $A$ ?

Solution:

Let $v$ be the velocity of sound along direction $\mathrm{AC}$ so it can reach $\mathrm{B}$ with resultant velocity $\mathrm{AD}$

Velocity along $A B=\sqrt{V^{2}-U^{2}}$

Time $=\frac{\text { distance }}{\text { speed }}$

$t=\frac{x}{\sqrt{V^{2}-U^{2}}}$

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