- #1

Grey_Thunderhead

- 7

- 0

## Homework Statement

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"An airplane is flying on a bearing of 340 degrees at 400mph. A wind is blowing at a bearing of 320 degrees at 30mph. Find ground speed and direction of the plane."

## Homework Equations

vx=vcosϕ

vy=vsinϕ

## The Attempt at a Solution

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First, my teacher told us to change from bearings to standard positions, so I did that. For the plane, I have that it is flying at 110 degrees. For the wind, I have that it is blowing at 130 degrees.

Knowing that, I calculated ground speed by doing the following:

(400cos110+30cos130)^2 + (400sin110+30sin130)^2

Then I took the square root of that and rounded to get a speed of about 428.214mph.

The issue, then, is finding the direction of the plane. I calculated the components of the plane's movement to be <-136.808,375.877> and the wind to be <-19.284,22.981>.

I then added them together for a total of <-156.092,398.858>.

I took the arctan of (398.858/-156.092) to try to get the angle, and I got -68.627 degrees. Now, I know I'm supposed to do something to this because it's not supposed to be negative, but I'm not sure where to go from here.

Are my calculations correct up to this point? If so, how do I use what I have now to find direction?

Thank you very much!