An airplane is headed on a bearing of 140° with an air speed of 500 miles per hour. The course has a bearing of 128°. The ground speed is 580 miles per hour. Find the drift angle, the wind direction, and the wind speed.
drift angle is clearly 12°
Make a sketch to have a triangle with sides 500 and 580 with 12° as the contained angle.
Using cosine law, let the third side be R (the wind speed)
R^2 = 500^2 + 580^2 - 2(500(580)cos12°
R = ....
then use the Sine Law to find one of the other angles , etc
580[128o] + Vw = 500[140o].
580*sin128+i580*Cos128 + Vw = 500*sin140+i500*Cos140.
457-357.1i + Vw = 321.4-383i,
Vw = 321.4-457-383i+357.1i = -135.6 - 25.9i = 138mi/h[79.2o]Cw from +Y-axis. = Velocity of the wind.
NOTE: For clockwise rotation from +Y-axis(Bearing), the X-component is found by multiplying by the sine of the angle.
Multiply by the cosine to fine the Y-component.
Tan A = X/Y instead of Y/X.
A plane is headed with a bearing of 200° an airspeed of 250 miles per hour, with a wind blowing to the direction of
To solve this problem, we need to use trigonometry and vector addition. Let's break it down step by step:
Step 1: Define the given information:
- Airplane's heading: 140°
- Airplane's airspeed: 500 miles per hour
- Course bearing: 128°
- Ground speed: 580 miles per hour
Step 2: Calculate the difference in direction:
The difference in direction between the airplane's heading and the course is called the drift angle. We can find it by subtracting the course bearing from the airplane's heading. In this case: drift angle = 140° - 128° = 12°.
Step 3: Calculate the wind speed and direction:
The wind vector can be inferred by comparing the difference between the airplane's airspeed and ground speed. Let's denote the wind's speed as "W" and its direction as "θ".
We can start by determining the horizontal component of the wind vector. Since the airplane is moving in a northeast direction, the horizontal component of the wind vector (W_horizontal) would be the difference between the ground speed and the airspeed, multiplied by the cosine of the drift angle:
W_horizontal = (Ground speed - Airspeed) * cos(drift angle)
= (580 - 500) * cos(12°)
Next, we need to find the vertical component of the wind vector:
Since the airplane is not ascending or descending according to the given information, the vertical component (W_vertical) would be zero.
Now, we can find the magnitude of the wind vector (W) using the formula:
W = sqrt(W_horizontal^2 + W_vertical^2)
Finally, to find the wind's direction (θ), we can use the formula:
θ = arctan(W_vertical / W_horizontal)
Substitute the values into the formulas, and we can find the wind speed and direction.
Note: Remember to convert the angles to radians if your calculator uses radians instead of degrees.
I hope this helps! Let me know if you have any further questions.