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## Homework Statement

You are traveling on an airplane. The velocity of the plane with respect to the air is 160 m/s due east. The velocity of the air with respect to the ground is 41 m/s at an angle of 30° west of due north.

1) What is the speed of the plane with respect to the ground?

## Homework Equations

V

_{AB}=V

_{AC}+V

_{BC}

Pythagorean theorem

Trigonometry

(Not so sure about these)

## The Attempt at a Solution

I know that V

_{PG}=V

_{PA}+V

_{AG}, but I'm not sure about how to break velocities into their components.

I kept V

_{PA}at 160 since it only moves in one dimension (only east), and I tried breaking up V

_{AG}as such:

41cos60i+41sin60j

(60 degrees since that is the angle formed when putting V

_{AG}tip to tail with V

_{PA})

Added to V

_{PA}:

236.507 m/s

In searching various forums (this seems a common hw question), I've seen very different solutions than mine, so I know mine is wrong.

Thanks a lot

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