Final answer:
The speed of the wind is 5.06 m/s, and the direction of the wind is west.
Step-by-step explanation:
To find the speed and direction of the wind, we can use vector addition. The velocity of the plane relative to the ground can be represented as a sum of two vectors: the velocity of the plane in still air and the velocity of the wind. We can use trigonometry to find the magnitudes of these vectors.
Given that the plane is heading into the wind at a velocity of 120 m/s at an angle of 20° west of north, we can calculate the magnitude of the plane's velocity in still air using the formula: magnitude of plane's velocity in still air = magnitude of plane's velocity relative to the ground / (cosine of the angle between the plane's velocity relative to the ground and the plane's velocity in still air).
Using this formula, we find that the magnitude of the plane's velocity in still air is approximately 125.06 m/s. Since the velocity of the wind is the difference between the plane's velocity relative to the ground and the plane's velocity in still air, we subtract the magnitude of the plane's velocity in still air from the magnitude of the plane's velocity relative to the ground to find the magnitude of the wind's velocity, which is approximately 5.06 m/s. Therefore, the speed of the wind is 5.06 m/s.
Since the plane is heading into the wind, the direction of the wind is opposite to the direction of the plane's velocity relative to the ground. Therefore, the direction of the wind is 180° opposite to the direction of the plane's velocity relative to the ground. So, the direction of the wind is west.