How Do You Calculate Displacement from Dallas to Chicago Using Vector Addition?

[bdh2991]

Homework Statement

A map suggests that Atlanta is d1 = 730 mi in a direction of θ1 = 5.12° north of east from Dallas. The same map shows that Chicago is d2 = 559 miles in a direction of θ2 = 21.0° west of north from Atlanta. Modeling the Earth as flat, use this information to find the displacement from Dallas to Chicago.

Homework Equations

trig functions

The Attempt at a Solution

i used the vector <65.1466, 727.087> for dallas to atlanta, and used the vector <521.87, 200.328> for atlanta to chicago. I added them together to get vector from dallas to chicago, then used the pythagorean theorem to get the resultant magnitude which was 719.542. The angle i got was 32.33 degrees by using inverse tangent of the dallas to chicago vector, then subtracted the 5.12 degrees to get the angle northeast of dallas. Still saying i have the wrong answer so I'm not sure what I'm doing wrong. please help

 

[Doc Al]

i used the vector <65.1466, 727.087> for dallas to atlanta, and used the vector <521.87, 200.328> for atlanta to chicago.

To start with, it looks like you have mixed up your x and y components. (Assuming you mean it as x, y, where +x is east and +y is north.) And you need to be careful with signs.

 

[bdh2991]

i see, so correcting my mistakes i should use <-200.3277, 521.8715> as my second vector. working the rest of the problem out accordingly gives me the resultant 788.7116 and the angle 41.9 degrees. i hope this is right, and also I'm still confused if i should use 41.9 degrees as the angle they are asking for or 41.9-5.12 = 36.78 as my answer?

 

[Doc Al]

i see, so correcting my mistakes i should use <-200.3277, 521.8715> as my second vector. working the rest of the problem out accordingly gives me the resultant 788.7116 and the angle 41.9 degrees.

What's that angle measured from?

i hope this is right, and also I'm still confused if i should use 41.9 degrees as the angle they are asking for or 41.9-5.12 = 36.78 as my answer?

Why would you subtract 5.12 ?

Express the angle as X degrees north of east (or equivalently, Y degrees east of north).

 

[bdh2991]

the angle would be 48.1 degrees north of east, correct?

 

[Doc Al]

the angle would be 48.1 degrees north of east, correct?

That sounds about right.