Calculating the necessary aircraft heading to counter a wind velocity and proceed along a desired bearing to a destination is a classic problem in aircraft navigation. It makes good use of the law of sines and the law of cosines. Suppose you wish to fly in a certain direction relative to the ground. The wind is blowing at 50mph at an angle of 40 degrees to that direction. Your plane is flying at 100mph with respect to the surrounding air. The situation is illustrated in this Figure (where your desired direction of travel is due East). wind G0mph plane 100Mph Then you head into the wind at an angle of ground X mph degrees (enter your value of a), and your ground speed is miles per hour (enter your value of 2). anot the angnle a and the law of cosines to get the ground speed.
Calculating the necessary aircraft heading to counter a wind velocity and proceed along a desired bearing to a destination is a classic problem in aircraft navigation. It makes good use of the law of sines and the law of cosines. Suppose you wish to fly in a certain direction relative to the ground. The wind is blowing at 50mph at an angle of 40 degrees to that direction. Your plane is flying at 100mph with respect to the surrounding air. The situation is illustrated in this Figure (where your desired direction of travel is due East). wind G0mph plane 100Mph Then you head into the wind at an angle of ground X mph degrees (enter your value of a), and your ground speed is miles per hour (enter your value of 2). anot the angnle a and the law of cosines to get the ground speed.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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Transcribed Image Text:Calculating the necessary aircraft heading to counter a wind velocity and proceed along a desired bearing to a destination is a classic
problem in aircraft navigation. It makes good use of the law of sines and the law of cosines. Suppose you wish to fly in a certain direction relative
to the ground. The wind is blowing at 50mph at an angle of 40 degrees to that direction. Your plane is flying at 100mph with respect to the
surrounding air. The situation is illustrated in this Figure (where your desired direction of travel is due East).
plane
100mph
wind
60mph
Then you head into the wind at an angle of
ground X mph
degrees (enter your value of a), and your ground speed is
miles per hour (enter your value of T).
Hint: Apply the Law of Sines to get the angle a and the law of cosines to get the ground speed.
Expert Solution
Step 1
Solution:
Let the angle between the plane speed and wind speed be beta and the ground speed vector be x.
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