How Do You Calculate Displacement from Dallas to Chicago Using Vectors?

AI Thread Summary
To calculate the displacement from Dallas to Chicago using vectors, one must consider the directions and distances provided. Atlanta is located 730 miles at 5 degrees north of east from Dallas, while Chicago is 560 miles at 21 degrees west of north from Atlanta. The Pythagorean theorem is not applicable unless the vectors are perpendicular. Instead, the Law of Cosines is suggested for this calculation, as it accounts for the angles between the vectors. This approach will yield the correct displacement between the two cities.
BeckyStar678
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Homework Statement



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 degrees west of north from atlanta. modeling the Earth as flat, use this info to find the displacement from dallas to chicago.



Homework Equations





The Attempt at a Solution



is this just using the pythagorean theorem. is it 7302 + 5602
 
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BeckyStar678 said:

Homework Statement



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 degrees west of north from atlanta. modeling the Earth as flat, use this info to find the displacement from dallas to chicago.



Homework Equations





The Attempt at a Solution



is this just using the pythagorean theorem. is it 7302 + 5602

Only if they are in direction at are right angle to each other.

Maybe you want the Law of Cosines?
 

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