# A butterfly is flying with a velocity

Question:

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

1. $3 \mathrm{~m}$

2. $20 \mathrm{~m}$

3. $12 \sqrt{2} \mathrm{~m}$

4. $15 \mathrm{~m}$

Correct Option: , 4

Solution:

$\vec{V}_{B W}=4 \sqrt{2} \cos 45 \hat{i}+4 \sqrt{2} \sin 45 \hat{j}$

$=4 \hat{i}+4 \hat{j}$

$\overrightarrow{\mathrm{V}}_{\mathrm{W}}=-\hat{\mathrm{j}}$

$\overrightarrow{\mathrm{V}}_{\mathrm{B}}=\overrightarrow{\mathrm{V}}_{\mathrm{BW}}+\overrightarrow{\mathrm{V}}_{\mathrm{W}}=4 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}$

$\overrightarrow{\mathrm{S}}_{\mathrm{B}}=\overrightarrow{\mathrm{V}}_{\mathrm{B}} \times \mathrm{t}=(4 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}) \times 3=12 \hat{\mathrm{i}}+9 \hat{\mathrm{j}}$

$\left|\vec{S}_{\mathrm{B}}\right|=\sqrt{(12)^{2}+(9)^{2}}=15 \mathrm{~m}$