# Homework Help: Some really confusing directions (and the world is flat!).

1. Aug 7, 2007

### niyati

A map suggests that Atlanta is 730 miles in a direction of 5.00 degrees north of east from Dallas. The same map shows that Chicago is 560 miles in a direction of 21.0 degrees west of north from Atlanta. Modeling the Earth as flat, use this information to find the displacement from Dallas to Chicago.

Equations:

Ax = Acos(angle)
Ay = Asin(angle)

(same for vector B)

[resultant vector] = ((Ax + Bx)^2 + (Ay + By)^2)

So far, I graphed each pathway on the same picture, so that the resultant vector would complete a triangle. From Dallas to Atlanta (vector A), the h.c. = 730cos85, and the v.c. = 730sin85.

For Atlanta to Chicago (vector B), I couldn't figure out which angle to use. 69 degrees or 111? I'm thinking 111 degrees, because if I draw the three cities, so that two tails of vectors stem from Atlanta and form a V-shape (as if the positive y-axis is equivalent to north, the postive x-axis is equivalent to east on a compass, and negative x-axis to west), the angle would be 111 degrees.

If this is true, I was planning on getting the h.c. and v.c of B, and adding up the h.c.'s of A and B, and the v.c.'s of A and B, to the the total h.c. and v.c of R. Once that is given, I can use Pythagorean Theorum to get the magnitude of R, which is the total displacement between Dallas and Chicago.

2. Aug 7, 2007

### PhanthomJay

You are using 85 degrees as the angle of vector A, which is the angle the vector makes with the vertical; the angle is 5 degrees above the horizontal (it is given that the vector is 5 degrees north of east). If you choose the x component as the cosine of the angle, you best use 5 degrees in your calcs. For vector B, you can use 111 degrees, and the plus or minus sign for the components will come out of that equation; or if you use 69 degrees, that's OK also, but then you have to decide using a sketch as to whether the components are plus or minus.

3. Aug 7, 2007

### niyati

Oh crap. I think I drew my picture wrong. The way I drew it was as if the problem said, "5.00 degrees east of north", which is, well, WRONG.

I'll redraw it and see what I come up with.

Thank you!

4. Aug 7, 2007

### niyati

Uhm, okay.

So, Rx = [730cos(5 degrees) + 560cos(111 degrees)], and Ry = [730sin(5 degrees) + 560sin(111 degrees)].

Thus, the resultant vector's magnitude would be the square root of both terms squared (which I actually forgot to add to the equation I put into my post).

Would this be correct?

5. Aug 8, 2007

### PhanthomJay

Yes, this would give you the correct magnitude of the resultant displacement. But you must now calculate the direction of the resultant displacement.