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

The given situation can be represented as

In the above figure, v₁ is the speed of wind and v₂₁ is the speed of butterfly with respect to wind.

So, v₂₁ can be given as

$\begin{array}{c}{\mathbf{v}}_{21}=4\sqrt{2}\cos {45}^{\circ }\hat{\mathrm{i}}+4\sqrt{2}\sin {45}^{\circ }\hat{\mathrm{j}}\\ =4\sqrt{2}\times \frac{1}{\sqrt{2}}\hat{\mathrm{i}}+4\sqrt{2}\times \frac{1}{\sqrt{2}}\hat{\mathrm{j}}=4\hat{\mathrm{i}}+4\hat{\mathrm{j}}\end{array}$

and v₁ can be given as

${\mathrm{v}}_1=-\hat{\mathrm{j}}$

$\therefore$ Velocity of butterfly can be given as

${\mathrm{v}}_2={\mathrm{v}}_1+{\mathrm{v}}_{21}=4\hat{\mathrm{i}}+4\hat{\mathrm{j}}-\hat{\mathrm{j}}=4\hat{\mathrm{i}}+3\hat{\mathrm{j}}$

$\therefore$ Displacement of butterfly, $\mathrm{D}={\mathrm{v}}_2\times \mathrm{t}$

                                                        $=(4\hat{\mathrm{i}}+3\hat{\mathrm{j}})\times 3=12\hat{\mathrm{i}}+9\hat{\mathrm{j}}$

$\therefore \text{ Magnitude of displacement, }\left|\mathrm{D}\right|=\sqrt{{12}^2+9^2}=15\mathrm{m}$