# Hard vector problem

1. Jun 13, 2010

### mandy9008

1. The problem statement, all variables and given/known data
A commuter airplane starts from an airport and takes the route shown in the figure below. The plane first flies to city A located 175 km away in a direction 30.0° north of east. Next, it flies for 150 km 20.0° west of north to city B. Finally, the plane flies 190 km due west, to city C. Find the location of city C relative to the location of the starting point.

2. Relevant equations

3. The attempt at a solution
I found the X and Y components of each vector (A, B, and C) and then added them to find the D components, which i then solved for D, the distance
Ax=175 cos 30 = 151.6
Ay=175 sin 30 = 87.5
Bx=150 cos 20 =140.9
By=150 sin 20 = 51.3
Cx=190 cos 180 = -190
Cy=190 sin 180 = 0

Dx=102.5
Dy=138.8

D=square root (138.8/102.5)
D=1.16

2. Jun 13, 2010

### Staff: Mentor

Re: Vectors

Did you draw a picture?
These are correct for the coordinates of city A.
These aren't correct, nor are the coordinates for city C. City A isn't at the origin, so you have to take the coordinates of A into account when you find the coordinates of city B.
Where did you get this formula?

3. Jun 14, 2010

### Redbelly98

Staff Emeritus
Re: Vectors

Mark44, it looks like Bx and By are not meant to be the coordinates of city B, rather they are the displacement components from A to B.

mandy9008, there are a couple of errors in your work. First, the angle for vector B is not 20°. You need to figure out the angle with respect to due east.

Also, you seem to be confusing the magnitude of a vector with the angle of the vector here:
Please look up the formulas for magnitude and angle of a vector in terms of its x and y components.