Final answer:
To find the bearing the pilot should fly and the plane's ground speed, we need to consider the effect of the wind on the plane's direction. By using vector addition and trigonometry, we can calculate these values. The pilot should fly at a bearing of 64° 30' - 180° + angle, and the plane's ground speed will be the magnitude of the resulting vector.
Step-by-step explanation:
To find the bearing the pilot should fly, we need to consider the effect of the wind on the plane's direction. The wind is blowing from the south at 35.0 mph. The desired flight path bearing is 64° 30', which is east of north. Since the wind is blowing from the south, it will push the plane slightly to the west.
To find the actual bearing, we can use vector addition. Let's assume the plane is flying at a speed of 1 mph and the wind is blowing at 1 mph. The resulting velocity vector will be the sum of the plane's velocity vector and the wind's velocity vector.
Using trigonometry, we can calculate the angle and magnitude of the resulting vector. The plane's actual bearing will be the angle of the resulting vector with the north direction. The plane's ground speed will be the magnitude of the resulting vector.
In this case, the wind is blowing from the south, so it has a bearing of 180°. The plane's desired bearing is 64° 30'. By subtracting the wind's bearing from the desired bearing, we can find the angle between the plane's heading and the wind. This angle can then be used to calculate the magnitude and direction of the resulting vector.
Finally, we can calculate the actual bearing the plane should fly by adding the wind's bearing to the angle between the plane's heading and the wind. The plane's ground speed will be the magnitude of the resulting vector.
In conclusion, the pilot should fly at a bearing of 64° 30' - 180° + angle, and the plane's ground speed will be the magnitude of the resulting vector.