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*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