Final answer:
To find the resultant velocity of the airplane, we can use vector addition. The airplane is heading due south at a speed of 540 km/h and the wind is blowing from the southwest at a speed of 80.0 km/h. The resultant velocity of the airplane is 596.6 km/h south.
Step-by-step explanation:
To find the resultant velocity of the airplane, we need to consider the airplane's velocity and the velocity of the wind. The airplane is heading due south at a speed of 540 km/h. The wind is blowing from the southwest at a speed of 80.0 km/h.
To find the resultant velocity, we can use vector addition. We can break down the airplane's velocity and the wind's velocity into their respective components.
Since the airplane is heading due south, its velocity has a magnitude of 540 km/h in the south direction. The wind is blowing from the southwest, which is 45 degrees west of south. The magnitude of the wind's velocity is 80.0 km/h, and its south component can be found using trigonometry: 80.0 km/h * sin(45) = 56.6 km/h.
The resultant velocity of the airplane is the vector sum of its velocity and the wind's velocity. The south component of the airplane's velocity (540 km/h) and the wind's south component (56.6 km/h) can be added together to get 596.6 km/h. Therefore, the resultant velocity of the airplane is 596.6 km/h south.