Question 190 of 308

A butterfly is flying with a velocity $4\sqrt{2}m{s}^{-1}$ in north-east direction. Wind is slowly blowing at $1m{s}^{-1}$ from north to south. The resultant displacement of the butterfly in $3$ seconds is:

A$3m$B$20m$C$12\sqrt{2}m$D$15m$

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Answer: (D) $15m$

${\vec{V}}_{BW}=4\sqrt{2}\cos 45\hat{i}+4\sqrt{2}\sin 45\hat{j}$
$=4\hat{i}+4\hat{j}$
${\vec{V}}_{w}=-\hat{j}$
${\vec{V}}_{B}={\vec{V}}_{BW}+{\vec{V}}_{w}=4\hat{i}+3\hat{j}$
${\vec{S}}_{B}={\vec{V}}_{B}\times t=(4\hat{i}+3\hat{j})\times 3=12\hat{i}+9\hat{j}$
$\left|{\vec{S}}_{B}\right|=\sqrt{(12{)}^{2}+(9{)}^{2}}=15m$