Final answer:
To find the speed and direction of the wind, we can use vector addition and trigonometry. The wind speed is 18.13 m/s and the wind direction is northeast.
Step-by-step explanation:
To find the speed and direction of the wind, we need to use vector addition. The airplane's velocity relative to the ground can be represented as a vector pointing northwest. We can break down this vector into its north and west components using trigonometry.
The north component is 38.0 * sin(45°) = 26.87 m/s and the west component is 38.0 * cos(45°) = 26.87 m/s. Since the airplane is heading north at 45.0 m/s, we can subtract the north component to find the wind speed: 45.0 - 26.87 = 18.13 m/s.
The wind direction can be found as the angle formed between the north component and the resultant vector (airplane velocity). Using trigonometry, we can find the angle as arctan(26.87/26.87) = 45°. Therefore, the wind is blowing from the northeast.