To determine the direction in which the pilot should aim the plane, we need to consider the vector addition of the airplane's velocity and the wind's velocity.
1. First, let's resolve the wind's velocity into its north and east components. Since the wind is blowing from the southwest, it forms a 45-degree angle with the south direction.
Using trigonometry, we can calculate the north and east components of the wind's velocity:
North component = wind speed * sin(45°)
= 110 km/h * sin(45°)
≈ 77.78 km/h
East component = wind speed * cos(45°)
= 110 km/h * cos(45°)
≈ 77.78 km/h
2. Now, let's consider the direction in which the plane is heading. The plane is heading due south, so its velocity vector only has a south component, which is equal to its speed.
Plane's south component = 734 km/h
3. To counteract the effect of the wind and maintain the plane's southward direction, the pilot needs to point the plane in the opposite direction of the wind's east and north components.
Plane's target heading:
South component = Plane's south component
= 734 km/h
North component = -North component of wind
= -77.78 km/h
East component = -East component of wind
= -77.78 km/h
4. Finally, we can calculate the direction by finding the angle between the southward velocity and the target heading.
Tanθ = North component / East component
Tanθ = (-77.78 km/h) / (-77.78 km/h)
Tanθ = 1
Since Tanθ = 1, the angle θ is 45 degrees.
Therefore, the pilot should aim the plane 45 degrees west of south in order to fly due south when there is a southwest wind blowing at 110 km/h.