A firecracker exploding on the surface of a lake is heard as two sounds a time interval t apart by a

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A firecracker exploding on the surface of a lake is heard as two sounds a time interval t apart by a man on a boat close to water surface. Sound travels with a speed u in water and a speed v in air. The distance from the exploding firecracker to the boat is

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Sol. t1 : time taken by sound to travel in watert2 : time taken by sound to travel in air.t1 = $\frac{d}{u}$t2 = $\frac{d}{v}$t2 – t1 = t (given)$\frac{d}{v} - \frac{d}{u} = t$$d\left\lbrack \frac{u - v}{uv} \right\rbrack = t$$d = \frac{uvt}{u - v}$

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