A planes actual resulting ground speed and direction are 550 mph and N26E. A wind is blowing from the northeast. If the pilot is holding a course of N27E how fast is the wind blowing?
if the wind speed is w and the plane's speed is s, then
(w cos-135°,w sin-135°)+(s cos63°, s sin63°) = (550 cos64°,550 sin64°)
-.707w + .454s = 241.104
-.707w + .891s = 494.337
w = 31.089
To determine the wind speed, we need to first understand the concept of ground speed and how it is affected by wind.
Ground speed refers to the actual speed at which the aircraft is moving relative to the ground. It is the combination of the plane's true airspeed (TAS) and the velocity of the wind.
In this case, we know that the plane's ground speed is 550 mph in the direction N26E. This means that, with no wind present, the plane would be traveling at 550 mph in the direction N26E.
However, there is a wind blowing from the northeast, which affects the ground speed and direction. To find the wind speed, we need to consider how the wind affects the plane's course.
The pilot is holding a course of N27E, which implies that the plane is heading in the direction N27E regardless of the wind. Since the wind is blowing in a different direction, it will cause the plane to drift from its intended course.
To calculate the wind speed, we need to analyze the difference between the actual course (N27E) and the resulting ground track (N26E). The difference between the two tracks is called the wind correction angle (WCA).
In this case, the difference between N27E and N26E is 1 degree, which means the wind is pushing the plane off course by 1 degree.
Now, we can calculate the wind speed using the formula:
Wind Speed = Ground Speed * tan(WCA)
Plugging in the given values, we have:
Wind Speed = 550 mph * tan(1 degree)
Using a scientific calculator or a trigonometric table, we find that the tangent of 1 degree is approximately 0.017455.
Wind Speed = 550 mph * 0.017455
Wind Speed ≈ 9.6 mph
Therefore, the wind speed is approximately 9.6 mph.