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Vectors Problem

  1. Nov 7, 2005 #1
    Tammy leaves the office, drives 26 km due north, then turns onto a 2nd highway and continues in a direction of 30.0 degrees north of east for 62 km. What is her total displacement from the office?
    The triangle I drew:
    |\
    |' \ a
    |b \
    |___\
    a = 62 km
    b = 26 km
    ' = 30 degrees
     
  2. jcsd
  3. Nov 8, 2005 #2

    cepheid

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    Staff Emeritus
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    Gold Member

    You seem to have her going southeast instead of northeast as it should be.
     
  4. Nov 8, 2005 #3
    ^ah...right. thanks.

    Would Dnet x = 62 cos 30 = 53.7 km
    Then Dnet y = 26 km + 62 cos 30 = 57 km
    Then total displacement:
    sqrt(53.7^2 + 57^2) = 78.3 km?
     
    Last edited: Nov 8, 2005
  5. Nov 8, 2005 #4
    Yep, thats one way to do it. You could also use the cosine law.

    x = [26^2 + 62^2 - 2(26)(62)(cos 120)] ^ .5
    x = 78.3
     
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