Ajet airliner moving initially at 858 mph (with respect to the ground) to the east moves into a region where the wind is blowing at 777 mph in a direction 38◦ north of east. what is the new speed of the aircraft with respect to the ground?

1546.2 mph

Explanation:

The new speed of the aircraft will be the magnitude of the resultant velocity due to the velocity of the aircraft + the velocity of the wind.

The components of the initial velocity of the jet are:

where we took east as positive x-direction and north as positive y-direction.

The components of the wind's velocity are

So the components of the resultant velocity are

And so, the new speed of the plane respect to the ground is

come closer and become far apart and become steam/gas

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