1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Vector Addition

  1. Apr 23, 2015 #1

    1. A ship sails 130 km due north from island A to island B and then 92 km, in the direction 22° south of east, to island C. The ship after that returns directly to island A. Calculate the magnitude and direction of the displacement vector in the last trip. Draw appropriate diagrams.

    2. Relevant equations

    3. The attempt at a solution

    I think I would find the total displacement and that would be equivalent to the last trip.

    D1 = X component = 0
    Y component = 130sin(90) = 130

    D2 = X component = 92cos(22) = 85.30
    Y component = 92sin(22) = 34.46 (-) as it is the - Y direction

    Adding the component together I get:

    Dx = 85.30
    Dy = 95.54

    Using the Pythagoras Theorem I get 128 km in a tan-1 (95.54/85.30) = 48.24 south of west direction. (Total displacement?)

    This makes sense to me when drawing it out. However, the only two answers I can find online give a way different solution that I can't comprehend, it is 56.44 km at 37.8 south of west. I figure i must be understanding the problem wrong but I can't for the life of me figure out how. Any help would be much appreciated.

  2. jcsd
  3. Apr 23, 2015 #2


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

    Hello, Brendan. Welcome to PF!

    Your answer looks correct for the question as stated. The other solution that you found online appears to be for a slightly different question where "22o south of east" is replaced by "22o east of south". But in that case, they should have stated the direction of the answer as 37.8o west of south rather than south of west.
    Last edited: Apr 23, 2015
  4. Apr 23, 2015 #3
    Thank you very much, I was confident in my answer but not confident enough. Cheers :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted