Aircraft Heading and Ground Speed
Sections
1. Simulation
2. Law of Sines
3. Simulation2
4. Law of Cosines
Sections
1. Simulation
2. Law of Sines
3. Simulation2
4. Law of Cosines
1. Simulation
Instructions Change the heading of the Airplane to collect the coin. Watch out, the wind will push you off course! Goals Change the Airplane Heading
Collect the Coin
| All degree measurements are given from north, clockwise. All magnitudes are in meters and velocities in meters/second
The light arrow is as long as the magnitude it represents. Dark arrows are guides.
Airplane Heading (Degrees From North) (0 to 360) |
2. Law of Sines
Instructions Read the text and answer the question. Goals Answer all questions
Submit your answers
| Wouldn't it be nice if there was an easier way to figure out what direction to point the airplane in to collect the coin?
Turns out there is! You can use the Law of Sines to figure out the angle between the Airplane's heading and the direction of the coin.
Then it's just simple subtraction to get the actual heading.
The wind direction is 133 Degrees. Hint: Angle B is the difference between the wind angle and the angle to the goal.
Give these questions a try. Look back at your notes or draw your own picture.
How many degrees is the angle A? (Round to two decimal places)
Hint Sin(A) = (Windspeed*Sin(B))/(Airspeed)
Subtract angle A from the direction of the goal(90 Degrees). What is the heading the airplane must take to reach the goal? (Round to two decimal places)
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3. Simulation2
Instructions Use the Law of Sines to find the heading of the Airplane to collect the coin, then change the Airspeed to match the required ground speed. Watch out, the wind will push you off course! Goals Solve for, and input the airplane heading
Change the airplane speed
Collect the coin at the required ground speed
| All degree measurements are given from north, clockwise. All magnitudes are in meters, speeds and velocities in meters/second
The Light arrow is as long as the magnitude it represents. Dark arrows are guides.
This time the airplane can't collect the coin unless it's ground speed (The speed the airplane is moving relative to the ground) is 25 m/s.
So, You'll have to modify the Airspeed (How fast the airplane is moving relative to the air it's flying in) to get a ground speed of 25 m/s. Airplane Heading (Degrees From North) (0 to 360) Airplane Speed (Airspeed) (m/s)
(0.0 to 100.0)
0
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4. Law of Cosines
Instructions Read the text and answer the question. Goals Answer all questions
Submit your answers
| Now that you have the Law of Sines to figure out the airplane's heading, you need a way to get the right groundspeed without all the trial and error.
That's where the Law of Cosines comes in. When you have two sides of a triangle and the angle between them, you can use the Law of Cosines to find the
third side.
The wind direction is 133 Degrees. Angle B is the difference between the wind angle and the angle to the goal.
Give these questions a try. Look back at your notes or draw your own picture.
How many degrees is the angle C? (Round to two decimal places)
Hint In a triangle the angles add to 180 degrees so, C = 180-B-A
Use the Law of Cosines to find the Groundspeed (Round to two decimal places)
Hint Groundspeed = Sqrt(Airspeed^2 + Windspeed^2 - 2*Airspeed*Windspeed*Cos(C))
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5. Lesson Done
Instructions You have completed the lesson. You may scroll up to review the lesson. |
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