Final answer:
To determine the maximum wind velocity for a 45° crosswind, we can use trigonometry and vector addition. The maximum crosswind component is given as 25 knots. By using the sine and cosine functions, we can find the perpendicular component of the wind velocity. Using the Pythagorean theorem, we can then calculate the magnitude and direction of the wind velocity.
Step-by-step explanation:
The maximum wind velocity for a 45° crosswind can be determined using the concept of vector addition. In this scenario, the airplane's velocity relative to the ground is 38.0 m/s at an angle of 20.0° west of north. The maximum crosswind component is given as 25 knots. To find the maximum wind velocity, we can use trigonometry to find the perpendicular component of the wind velocity and then calculate the magnitude and direction of the wind velocity.
First, we need to find the crosswind component using the sine function: crosswind component = maximum crosswind x sin(45°) = 25 knots x sin(45°) = 17.68 knots. Now, we can find the perpendicular component of the wind velocity by using the cosine function: perpendicular component = crosswind component x cos(45°) = 17.68 knots x cos(45°) = 12.50 knots.
Finally, we can use the Pythagorean theorem to find the magnitude of the wind velocity: magnitude of wind velocity = √(perpendicular component^2 + maximum crosswind^2) = √(12.50 knots^2 + 25 knots^2) ≈ 27.34 knots. The direction of the wind can be determined by finding the arc-tangent of the ratio of the perpendicular component to the maximum crosswind: direction of wind = atan(perpendicular component / maximum crosswind) = atan(12.50 knots / 25 knots) ≈ 26.57°. Therefore, the maximum wind velocity for a 45° crosswind is approximately 27.34 knots at a direction of 26.57°.