A firecracker exploding on the surface of a l | vedclass

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Question

(A) Let $d$ be the distance between the firecracker and the boat.The sound travels through water with speed $u$ and through air with speed $v$.The tim

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) Let $d$ be the distance between the firecracker and the boat.The sound travels through water with speed $u$ and through air with speed $v$.The time taken for sound to reach the boat through water is $t_1 = \frac{d}{u}$.The time taken for sound to reach the boat through air is $t_2 = \frac{d}{v}$.Given that the time interval between the two sounds is $t$,we have $t_2 - t_1 = t$ (since $v  t_1$).Substituting the expressions: $\frac{d}{v} - \frac{d}{u} = t$.Factor out $d$: $d \left( \frac{u - v}{uv} \right) = t$.Solving for $d$: $d = \frac{uvt}{u - v}$.

Column-$I$	Column-$II$
$(a)$ Transverse wave through a steel rod	$(i)$ $\sqrt{B + \frac{4}{3} \frac{\eta}{\rho}}$
$(b)$ Longitudinal waves in earth's crust	$(ii)$ $\sqrt{\frac{\eta}{\rho}}$
$(c)$ Longitudinal waves through a steel rod	$(iii)$ $\sqrt{\frac{2 \pi T}{g \lambda}}$
$(d)$ Ripples	$(iv)$ $\sqrt{\frac{Y}{\rho}}$

$A$ 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 the 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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