To determine the resultant velocity of the airplane, taking into account the wind, we can use vector addition.
Let's break down the velocities into their components:
The airspeed of the airplane is 600 km/hr, heading north. Since it's heading directly north, the vertical component of its velocity is 600 km/hr.
The wind is blowing from the northeast, which can be broken down into its horizontal and vertical components. We can use trigonometry to calculate these components.
The wind is blowing at a speed of 40 km/hr. Let's denote the horizontal component as Wx and the vertical component as Wy.
The wind is coming from the northeast, which is a 45-degree angle between the north and east directions. Using the angle and the given speed of the wind, we can find the components:
Wx = 40 km/hr * cos(45°)
Wy = 40 km/hr * sin(45°)
Calculating these values:
Wx ≈ 28.28 km/hr
Wy ≈ 28.28 km/hr
To find the resultant velocity, we can add the components of the airplane's airspeed and the wind:
Vx = 0 km/hr + 28.28 km/hr ≈ 28.28 km/hr (eastward)
Vy = 600 km/hr + 28.28 km/hr ≈ 628.28 km/hr (northward)
The resultant velocity of the airplane, taking into account the wind, is approximately 28.28 km/hr eastward and 628.28 km/hr northward.