A firecracker exploding on the surface of a lake is heard as two … - Vidyadip

MCQ

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

A
$\frac{{uvt}}{{u + v}}$
B
$\frac{{t(u + v)}}{{uv}}$
C
$\frac{{t(u - v)}}{{uv}}$
✓
$\frac{{uvt}}{{u - v}}$

✓

Answer

Correct option: D.

$\frac{{uvt}}{{u - v}}$

d
$\mathrm{d}=\mathrm{ut}_{0}$

$\Rightarrow \mathrm{d}=\mathrm{v}\left(\mathrm{t}_{0}+\mathrm{t}\right)$

$\Rightarrow(v-u) t_{0}+v t=0$

$t_{0}=\frac{v t}{u-v}$

$d=\frac{u v t}{u-v}$

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