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Vectors i guess

  1. Jun 3, 2006 #1
    Long John Silver, a pirate, has buried his treasure on an island with five trees located at the following points: A (30.0 m, -20.0 m), B (60.0 m, 80.0 m), C (-10.0 m, -10.0 m), D (40.0 m, -30.0 m), and E (-70.0 m, 60.0 m). All of the points are measured relative to some origin. Long John's map instructs you to start at A and move toward B, but cover only one-half the distance between A and B. then move toward C, covering one-half the distance between your current location and C. Then move toward D, covering one-fifth the distance between where you are and D. Finally, move toward E, covering one-fifth the distance between you and E, stop, and dig.

    What are the coordinates of the point where the pirate's treasure is buried?

    i added all the x's and y's (following the rules of above) and got x 49 and y = 21

    i got the problem wrong..so what am i doing wrong?


    the question also says that you can rearrange the order of the trees - for instance, B (30 m, -20 m), A (60 m, 80 m), E (-10 m, -10 m), C (40 m, -30 m), and D (-70 m, 60 m) - and repeat the calculation to show that the answer does not depend on the order....i did the latter and still got the problem wrong.....

    plz help
     
  2. jcsd
  3. Jun 3, 2006 #2

    Doc Al

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    Staff: Mentor

    Why don't you spell out your intermediate steps along the way so we can see where you might have made an error.
     
  4. Jun 3, 2006 #3
    k...so i have
    Ax = 30
    Ay= -20

    Bx = 60
    By = 80 half the distance from A to B would be adding (60/2) to Ax and (80/2) to Ay...so now im at (60,20)

    Cx = -10
    Cy = -10 half the distance from (60,20) to C would be adding (-10/2) to 60 and (-10/2) to 20...so now im at (55,15)

    dx = 40 (1/5) the distance from (55,15) to D gives me (63,9)
    dy = -30

    Ex = -70
    Ey = 60 (1/5) the distance from (63,9) to E gives me (49,21) as my final point
     
  5. Jun 3, 2006 #4
    The keyword here is "half the distance from A to B"

    You are dividing the coordinate of point B by two, then adding to A..which is wrong.

    You first need to find the distance, or the VECTOR AB

    broken down into components:
    Bx - Ax = ABx
    By - Ay = ABy

    which is simply:

    60-30 = 30 = ABx
    80-(-20)=100 = ABy
    vecotr AB = <30,100>

    Now, divide both the vector by two, or multiply by (1/2)

    vectorAB/2 will result in the components <15,50>

    now take that vector and add that to the coordinate of point A

    ( (30+15), (-20+50) ) = (45,30) is the point halfway from point A to B, or "half the distance from A to B"



    Of course you could simply use the midpoint forumula

    pt = ((x1+x2)/2, (y1+y2)/2))..and that will be the same result...
     
    Last edited: Jun 3, 2006
  6. Jun 3, 2006 #5
    k i followed ur steps and got (3.6,13.6)...can somebody please confirm my answer....also, when finding the (1/5th) distance between two points could you use (x1+x2)/5, y1+y2/5....i tried this but i got conflicting numbers compared to doing it the other way...
     
  7. Jun 4, 2006 #6

    Doc Al

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    Staff: Mentor

    No. Adding 1/5 of the distance (just like adding half the distance) means:
    x1 + (x2 - x1)/5; y1 + (y2 - y1)/5.

    Of course, adding half the distance is a special case, since:
    x1 + (x2 - x1)/2 = (x1 + x2)/2, but that won't work in general.
     
  8. Jun 4, 2006 #7
    like i said earlier, i got (3.6,13.6) as my final answer from using tekken's method...did i get it right?
     
  9. Jun 4, 2006 #8

    Doc Al

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    Staff: Mentor

    Looks good to me.
     
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