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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$\mathrm{d}=\mathrm{ut}_{0}$
$\Rightarrow \mathrm{d}=\mathrm{v}\left(\mathrm{t}_{0}+\mathrm{t}\right)$
$\Rightarrow(v-u) t_{0}+v t=0$
$t_{0}=\frac{v t}{u-v}$
$d=\frac{u v t}{u-v}$
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