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Math Help - HMRK Question (Vectors)

  1. #1
    Mtl
    Mtl is offline
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    HMRK Question (Vectors)

    A boater wishes to cross the canal which is 3.0km wide. He wishes to land at a point 2.0km upstream from his starting point. If the current in the canal flows at 3.5km/h and the speed of the boat is 13km/h
    (a) what course should he steer
    (b) how long will his trip take

    Ok, I'm having a "dumb" moment right now and I'm kind of blanking. Could someone show me how to do part A, as once that is determined part B becomes pretty trivial.
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  2. #2
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    Let  \theta be the angle between where the boater points his boat and directly across the stream. Let t be the time taken to cross.

    Then resolve into perpendicular components parallel to and perpendicular to the stream:
    <br />
13 \cos (\theta )t = 3
    13 \sin (\theta )t - 3.5t = 2.

    Now you can solve simultaneously.
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