An airplane is headed southwest (bearing 225°) with an air speed of 550 miles per hour, with the wind blowing from the northwest (bearing 135°) at a speed of 110 miles per hour. Find the drift angle, ground speed, and the course of the airplane.

planes fly headings, not bearings.

Turn your data into vectors. Add the vectors, and convert back to speed and heading.

550@225° = <-389,-389>
110@135° = <78,-78>
So, the resultant velocity is <-311,-467> = 561@214°

I'll leave the drift angle up to you. Draw a diagram of the vectors involved.

Vr = 550mi/h[225o] + 110mi/h[135o].

X = 550*sin225 + 110*sin135 = -311.1 mi/h.
Y = 550*Cos225 + 110*Cos135 = -466.7 mi/h.

Vr = -311.1 - 466.7i = 561mi/h[33.7o] = 561mi/h[214o]CW(Bearing) =
Resultant velocity and Direction.

Drift = 225-214 =

Note: 33.7o W. of S. = 214o CW from +Y-axis.

To find the drift angle, ground speed, and course of the airplane, we can use vector addition and trigonometry.

1. Start by drawing a diagram to visualize the situation. Draw a line to represent the heading of the airplane, pointing southwest (225°). Label it as vector A.
2. Draw another line to represent the wind direction, blowing from the northwest (135°). Label it as vector B.
3. Now, we need to find the resultant vector (vector C) by adding vectors A and B. To do this, we can break down vectors A and B into their horizontal and vertical components.

- For vector A: determine the horizontal component by multiplying the airspeed (550 mph) by the cosine of the bearing (225°). The vertical component is obtained by multiplying the airspeed by the sine of the bearing.
- For vector B: determine the horizontal component by multiplying the wind speed (110 mph) by the cosine of the bearing (135°). The vertical component is obtained by multiplying the wind speed by the sine of the bearing.

4. Add the horizontal components of vectors A and B to find the horizontal component of vector C.
5. Add the vertical components of vectors A and B to find the vertical component of vector C.
6. The drift angle (θ) can be calculated by taking the inverse tangent of the vertical component divided by the horizontal component: θ = arctan(vertical component/horizontal component).
7. The ground speed can be calculated by taking the square root of the sum of the squares of the horizontal and vertical components of vector C.
8. The course of the airplane can be calculated by taking the inverse tangent of the vertical component divided by the horizontal component of vector C and adding 180°.

Let's calculate the drift angle, ground speed, and course of the airplane using the given values:

Horizontal component of A = airspeed x cos(bearing of A) = 550 mph x cos(225°)
Vertical component of A = airspeed x sin(bearing of A) = 550 mph x sin(225°)

Horizontal component of B = wind speed x cos(bearing of B) = 110 mph x cos(135°)
Vertical component of B = wind speed x sin(bearing of B) = 110 mph x sin(135°)

Horizontal component of C = horizontal component of A + horizontal component of B
Vertical component of C = vertical component of A + vertical component of B

Drift angle (θ) = arctan(vertical component of C/horizontal component of C)
Ground speed = sqrt((horizontal component of C)^2 + (vertical component of C)^2)
Course of the airplane = arctan(vertical component of C/horizontal component of C) + 180°