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?

1546.1 mph

Explanation:

Let's take the east direction as positive x-direction and north as positive y-direction.

The components of the initial velocity of the jet are:

while the components of the wind's velocity are

So, the components of the new velocity of the jet are:

And therefore, the new speed is the magnitude of the new velocity, so: