Ajet airliner moving initially at 406 mph (with respect to the ground) to the east moves into a region where the wind is blowing at 568 mph in a direction 15◦ north of east. what is the new speed of the aircraft with respect to the ground?

966 mph

Explanation:

Using as convention:

- East --> positive x-direction

- North --> Positive y-direction

The x- and y- components of the initial velocity of the jet can be written as

While the components of the velocity of the wind are

So the components of the resultant velocity of the jet are

And the new speed is the magnitude of the resultant velocity:

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