AP Physics Problem - Highway between two cities

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Homework Help Overview

The problem involves determining the shortest length of a highway between two towns located at specific coordinates, as well as the angle of the highway with respect to due west. The context is rooted in geometry and trigonometry, particularly the Pythagorean theorem.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the use of the Pythagorean theorem for calculating the distance and raise questions about the interpretation of the angle with respect to due west. There is also a consideration of whether the Earth can be assumed flat for this problem.

Discussion Status

Some participants have provided initial calculations and interpretations, while others are exploring the ambiguity in the phrasing of the angle question. There is an acknowledgment of multiple interpretations regarding the angle measurement, and a suggestion to seek clarification from an instructor has been made.

Contextual Notes

Participants note the lack of clarity in the problem statement regarding which city serves as the origin for angle measurement, which may affect the interpretation of the angle calculation.

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Homework Statement


A highway is to be built between two towns, one of which lies 40.7 km south and 72.5 km west of the other. (a) What is the shortest length of highway that can be built between the two towns, and (b) at what angle would this highway be directed, as a positive angle with respect to due west?

Homework Equations



No equations are given. I used Pythagorean theorem.

The Attempt at a Solution


I got 83.14m for the first part. I got 29.31 degrees for the second part but I don't think this is right.

THANK YOU SO MUCH FOR YOUR HELP!

PICTURE: https://www.dropbox.com/s/052vjjh3by6kbnl/Untitled.png?dl=0
 
Last edited:
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Are you allowed to assume the Earth is flat? I'm guessing you are, otherwise this become a spherical geometry problem.

How did you arrive at your answers? Did you draw a picture?
 
Yes we can assume the Earth is flat. The first part is simple, just Pythagorean theorem, really my question is about part B. I am confused when it says "with respect to due west". I added a picture to the post to show you what I have.
 
Ah, reading this question again, that is a very ambiguous way to phrase the question b, since it does not tell you which city is to serve as the origin.

There are two ways to interpret this question. Either it's asking for angle ABC or or angle 180°-ABC.

I don't think I can decipher which the question is asking for. Could you perhaps ask an instructor?
 

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