Question

A butterfly is flying with a velocity $4 \sqrt{2} m / s$ in North-East direction. Wind is slowly blowing at $1\, m / s$ from North to South. The resultant displacement of the butterfly in $3$ seconds is :

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

Answer 1

Answer: (D)

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