1. Resolve the butterfly's velocity into components

The butterfly flies with speed $4\sqrt{2}\ \text{m/s}$ in the North-East direction.

North-East means equal components toward North and East, so:

$v_{bx} = 4\ \text{m/s} \quad (\text{East})$ $v_{by} = 4\ \text{m/s} \quad (\text{North})$

because

$\frac{4\sqrt{2}}{\sqrt{2}} = 4$

So butterfly's velocity vector is:

$\vec v_b = 4\hat i + 4\hat j$

2. Write the wind velocity

Wind is blowing at $1\ \text{m/s}$ from North to South.

So the wind velocity is toward South:

$\vec v_w = -1\hat j$

3. Find the resultant velocity of the butterfly

Assuming the butterfly's ground velocity is the vector sum of its own velocity and wind velocity:

$\vec v = \vec v_b + \vec v_w$ $\vec v = (4\hat i + 4\hat j) + (-1\hat j)$ $\vec v = 4\hat i + 3\hat j$

Its magnitude is:

$|\vec v| = \sqrt{4^2 + 3^2} = \sqrt{16+9} = 5\ \text{m/s}$

4. Find the displacement in 3 seconds

Since the velocity is constant, displacement magnitude in $3$ s is:

$s = vt = 5 \times 3 = 15\ \text{m}$

5. Match with the options

$15\ \text{m}$

So the correct option is:

D: $15$ m

6. Comparison with stored correct answer

Stored correct answer is D, which matches the derived answer.