To determine the direction of the fluttering of the flag on the mast of the boat, we need to consider both the wind's direction and the boat's movement. The wind is blowing at a speed of 72 km/h towards the northeast (N.E), while the boat is moving north at a speed of 51 km/h. Let's break this down step by step.
Understanding the Wind and Boat Movement
The wind's direction is crucial here. When we say the wind is blowing from the northeast, it means that the wind is coming from the northeast and moving towards the southwest. Therefore, the effective direction of the wind relative to the boat will change once the boat starts moving.
Visualizing the Directions
- Wind Direction: Northeast (N.E) means the wind is coming from 45 degrees on a compass.
- Boat Direction: The boat is moving directly north (0 degrees).
Combining the Directions
To find the resultant direction of the wind relative to the boat, we can visualize this as a vector addition problem. The wind's vector points towards the southwest, while the boat's vector points north. Since the boat is moving north, we need to consider how the wind affects the flag's fluttering direction.
Calculating the Resultant Vector
We can break down the wind's speed into its components. The wind blowing at 72 km/h towards the northeast can be split into two components:
- Eastward component: 72 km/h * cos(45°) = 72 km/h * 0.7071 ≈ 50.91 km/h
- Northward component: 72 km/h * sin(45°) = 72 km/h * 0.7071 ≈ 50.91 km/h
Now, since the boat is moving north at 51 km/h, we can add the northward components:
- Total northward speed = Boat's speed + Wind's northward component
- Total northward speed = 51 km/h + 50.91 km/h ≈ 101.91 km/h
Determining the Flag's Fluttering Direction
With the boat moving north and the wind blowing from the northeast, the flag will flutter in the direction of the resultant wind vector. Since the wind has a significant eastward component, the flag will not only flutter north but also slightly towards the east. Therefore, the flag will flutter in a direction that is slightly east of north.
Conclusion
In summary, as the boat moves north at 51 km/h while the wind blows from the northeast at 72 km/h, the flag on the mast will flutter in a direction that is slightly east of north. This is due to the combined effect of the wind's eastward component and the boat's northward movement.
