Answer:
To determine the direction in which the plane should head to end up going due south, we need to consider the combined effect of the airplane's airspeed and the wind speed and direction.
Given:
Airspeed of the plane = 650 km/hr
Wind speed = 70 km/hr
Wind direction = From the southwest
To find the resulting direction, we can use vector addition. Let's break down the velocities into their components:
Airspeed of the plane:
Horizontal component = 650 km/hr (since the plane is flying due south, there is no horizontal component)
Wind velocity:
Horizontal component = 70 km/hr * cos(225°) (since the wind is coming from the southwest)
Vertical component = 70 km/hr * sin(225°)
Now let's add the horizontal and vertical components separately:
Horizontal component: 0 km/hr + 70 km/hr * cos(225°)
Vertical component: 650 km/hr + 70 km/hr * sin(225°)
Calculating the resulting direction using trigonometry:
Resulting direction = arctan(Vertical component / Horizontal component)
After performing the calculations, the resulting direction is approximately 182.12°. This direction is south of west.
Comparing the options provided:
- At an angle 3\<θ\<5 degrees south or west: This option does not align with the calculated resulting direction of approximately 182.12°.
- At an angle θ\<3 degrees south of west: This option aligns with the calculated resulting direction of approximately 182.12°.
- At an angle 3\<θ\<5 degrees west of south: This option does not align with the calculated resulting direction of approximately 182.12°.
- At an angle θ\<3 degrees west of south: This option does not align with the calculated resulting direction of approximately 182.12°.
Therefore, the correct option is: "At an angle θ\<3 degrees south of west." This aligns with the calculated resulting direction of approximately 182.12°.