Question

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

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

Answer 1

The correct option is D $15\text{m}$


In the figure,

${\overrightarrow{V}}_{BW}=\text{Velocity of butterfly in the frame of wind}$

${\overrightarrow{V}}_{WG}=\text{Velocity of wind in the frame of ground}$

We know that,

${\overrightarrow{V}}_{BW}={\overrightarrow{V}}_{BG}-{\overrightarrow{V}}_{WG}$

$\Rightarrow {\overrightarrow{V}}_{BG}={\overrightarrow{V}}_{BW}+{\overrightarrow{V}}_{WG}$

$\therefore V_{BG}=\sqrt{V_{BW}^2+V_{WG}^2+2V_{BW}{V}_{WG}\cos \theta }$

$\Rightarrow V_{BG}=\sqrt{(4\sqrt{2}{)}^2+1^2+2(4\sqrt{2}\left)\right(1\left)\cos \right({90}^{\circ }+{45}^{\circ })}$

$\Rightarrow V_{BG}=5\text{m/s}$

So, displacement in $3$ seconds,

$d=V_{BG}t=5\times 3=15\text{m}$

Hence, option $\left(D\right)$ is the correct answer.