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AP Physics Problem - Highway between two cities

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  1. Sep 4, 2014 #1
    1. The problem statement, all variables and given/known data
    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?


    2. Relevant equations

    No equations are given. I used Pythagorean theorem.

    3. 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: Sep 4, 2014
  2. jcsd
  3. Sep 4, 2014 #2

    Matterwave

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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?
     
  4. Sep 4, 2014 #3
    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.
     
  5. Sep 4, 2014 #4

    Matterwave

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    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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