The pilot of an aircraft wishes to fly due west in a 42.7 km/h wind blowing toward the south. The speed of the aircraft in the absence of a wind is 204 km/h.
North component of air speed must be 42.7
If angle west of north is T
204 cos T = 42.7
T = cos^-1 (42.7/204)
T = 78 degrees west of north or 12 degrees north of west
To determine the heading the pilot should take to fly due west in a crosswind, you need to break down the wind velocity into its components.
Let's consider the wind velocity as a vector with a magnitude of 42.7 km/h and a direction blowing toward the south. Since the pilot wants to fly due west, we need to determine the component of the wind that acts perpendicular to the desired direction.
To find this component, we can use trigonometry. In this case, we have a right triangle where the hypotenuse represents the wind velocity of 42.7 km/h, one side represents the component acting toward the south, and the other side represents the component acting perpendicular to the desired direction (west).
The angle between the desired direction (west) and the direction of the wind can be found using trigonometry as well. We can use arctan to find the angle, which will help determine the value of the component acting perpendicular to the desired direction.
Once we have the wind component acting perpendicular to the desired direction, we can subtract it from the aircraft's speed in the absence of wind (204 km/h) to determine the speed at which the pilot should fly in order to counteract the crosswind and maintain a due west heading.
So, let's calculate it step by step:
Step 1: Find the component of the wind acting perpendicular to the desired direction.
- The angle between the desired direction (west) and the direction of the wind can be found using trigonometry.
- Let's call this angle θ.
- Using arctan, we can calculate θ:
θ = arctan(42.7 km/h / 204 km/h)
Step 2: Calculate the component of the wind acting perpendicular to the desired direction.
- The component acting toward the south is given by:
south component = 42.7 km/h * sin(θ)
Step 3: Determine the speed the pilot should fly to counteract the crosswind.
- The speed of the aircraft in the absence of wind is 204 km/h.
- The component acting perpendicular to the desired direction (west) is given by:
west component = 204 km/h - south component