Given information:
- Velocity of butterfly = 4√2 m/s in North-East direction
- Wind velocity = 1 m/s from North to South
- Time = 3 seconds

Step 1: Analyzing the given information
To find the resultant displacement of the butterfly, we need to consider both the velocity of the butterfly and the velocity of the wind. The velocity of the butterfly is given as 4√2 m/s in the North-East direction, which means it is moving in a direction that is 45 degrees east of the North. The wind is blowing from North to South with a velocity of 1 m/s.

Step 2: Breaking down the velocities into components
To calculate the resultant displacement, we need to break down the velocities into their respective components. The velocity of the butterfly can be broken down into its North and East components using trigonometry.

Velocity of butterfly = 4√2 m/s
North component = 4√2 * sin(45 degrees) = 4 m/s
East component = 4√2 * cos(45 degrees) = 4 m/s

The wind velocity is purely in the North direction, so its North component is 1 m/s and its East component is 0 m/s.

Step 3: Adding the components
To find the resultant displacement, we need to add the North and East components of both the butterfly and the wind velocities.

North component = 4 m/s + 1 m/s = 5 m/s
East component = 4 m/s + 0 m/s = 4 m/s

Step 4: Calculating the resultant displacement
To calculate the resultant displacement, we can use the Pythagorean theorem.

Resultant displacement = √(North component)^2 + (East component)^2
Resultant displacement = √(5 m/s)^2 + (4 m/s)^2
Resultant displacement = √25 m^2/s^2 + 16 m^2/s^2
Resultant displacement = √41 m^2/s^2
Resultant displacement ≈ 6.40 m/s

Step 5: Conclusion
The resultant displacement of the butterfly in 3 seconds is approximately 6.40 m/s. This means that after 3 seconds, the butterfly would have traveled a distance of 6.40 meters in a direction that is 45 degrees east of the North.

Ans 15m