Final answer:
To find the speed and direction of the wind, we can use vector addition and trigonometric functions.
Step-by-step explanation:
To determine the speed and direction of the wind, we can use vector addition. First, we need to break down the velocity relative to the ground into its north and west components. The north component is 38.0 m/s and the west component can be found using trigonometry: 38.0 m/s * sin(45°) = 26.9 m/s. Next, we subtract the north component of the airplane's velocity (45.0 m/s) to find the wind's north component: 45.0 m/s - 38.0 m/s = 7.0 m/s. Lastly, to find the wind's direction, we can use the inverse tangent function: tan^(-1)(26.9 m/s / 7.0 m/s) ≈ 73.9° west of north.