Next: Newton's laws of motion Up: Motion in 3 dimensions Previous: Worked example 3.4: Hail

## Worked example 3.5: Flight UA589

Question: United Airlines flight UA589 from Chicago is 20miles due North of Austin's Bergstrom airport. Suppose that the plane is flying at relative to the air. Suppose, further, that there is a wind blowing due East at . Towards which compass bearing must the plane steer in order to land at the airport?

Answer: The problem in hand is illustrated in the diagram.
The plane's velocity relative to the ground is the vector sum of its velocity relative to the air, and the velocity of the wind relative to the ground. We know that is directed due East, and we require to be directed due South. We also know that and . Now, from simple trigonometry,

Hence,

However, it is clear from the diagram that the compass bearing of the plane is given by

Thus, in order to land at Bergstrom airport the plane must fly towards compass bearing .

Next: Newton's laws of motion Up: Motion in 3 dimensions Previous: Worked example 3.4: Hail
Richard Fitzpatrick 2006-02-02