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(B) In the figure,$\overline{AB}$ is a tree and $C$ and $D$ represent two positions of the boat.Suppose the constant velocity of the boat is $v 	ext{

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(B) In the figure,$\overline{AB}$ is a tree and $C$ and $D$ represent two positions of the boat.Suppose the constant velocity of the boat is $v 	ext{ m/min}$ and the boat takes time $t 	ext{ min}$ to reach from $D$ to $B$.Let $AB = h$.Now,according to the formula,$	ext{Distance} = 	ext{Speed} 	imes 	ext{Time}$,$CD = 10v$ and $BD = vt$.Now,in $\Delta ABD$,$	an 60^{\circ} = \frac{AB}{BD}$.$	herefore \sqrt{3} = \frac{h}{vt} \implies h = vt\sqrt{3} \quad ....(1)$In $\Delta ABC$,$	an 30^{\circ} = \frac{AB}{BC}$.$	herefore \frac{1}{\sqrt{3}} = \frac{h}{vt + 10v} \implies h = \frac{vt + 10v}{\sqrt{3}} \quad ....(2)$Equating $(1)$ and $(2)$,$vt\sqrt{3} = \frac{vt + 10v}{\sqrt{3}}$$3vt = vt + 10v$$2vt = 10v$$t = 5$.Thus,the boat takes $5$ minutes to reach the bank.

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