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Morphing Triangle Problem

  1. Oct 15, 2007 #1
    1. Two boats start out 800 miles apart with boat A directly to the west of boat B. At the same time both boats start moving with boat A travelling to the east at 40mph while boat B travels north at 20mph. Determine if the distance between the boats is increasing, decreasing, or not changing after the following travel times: (a) 7 hours (b) 16 hours (c) 25 hours

    2. I attempted to break apart their distances travelled by using component vector analysis. The distance between the two boats is the hypotenuse of whatever triangle they produce on the graph at a certain time. We want to find d'.

    3. d'=? I park boat A at origin, therefore its cartesian coordinates are (0, 0), so boat B must be at (0, 800)

    For part (a) I use vector components: A in x-direction: 400(7)=280 x-direction
    So A is at (280, 0) since it does change in relation to y-axis (vice-versa for B)
    B in y-direction: 20(7)=140 so B is (800, 140)
    Base distance is 800-280=520 Height is just 140
    I got the distance between them by using the distance formula: d=square root(520^2 + 140^2)= 538.516miles

    How do I proceed to find h' ?
  2. jcsd
  3. Oct 15, 2007 #2
    From what I know, we can not use properties of similar triangles since the boats are moving at different rates.
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