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

The butterfly flies in the north-east direction at $$4\sqrt{2}$$ m s$$^{-1}$$. Resolving this into components: the northward component is $$4\sqrt{2} \cdot \cos 45° = 4$$ m s$$^{-1}$$ and the eastward component is $$4\sqrt{2} \cdot \sin 45° = 4$$ m s$$^{-1}$$.

The wind blows from north to south at 1 m s$$^{-1}$$, adding $$-1$$ m s$$^{-1}$$ to the northward component. The resultant velocity of the butterfly is: eastward = 4 m s$$^{-1}$$, northward = $$4 - 1 = 3$$ m s$$^{-1}$$.

The magnitude of the resultant velocity is $$v = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5$$ m s$$^{-1}$$.

The resultant displacement in 3 seconds is $$d = v \times t = 5 \times 3 = 15$$ m.