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Kayaker paddling across a harbor

  1. Sep 14, 2012 #1
    1. The problem statement, all variables and given/known data

    A kayaker needs to paddle north across a 105 m wide harbor. The tide is going out, creating a tidal current that flows to the east at 1.5 m/s. The kayaker can paddle with a speed of 3.4 m/s.

    (a) In which direction should he paddle in order to travel straight across the harbor? (degrees west of north)

    (b) How long will it take him to cross? (seconds)

    2. Relevant equations

    c^2= a^2 + b^2

    3. The attempt at a solution

    I divided 105m by 3.4 m/s to determine how long it would take to go straight across the harbor. Then I multiplied that number (30.88) by 1.5 m/s to get the distance he would have ended up downstream. 46.32m.

    Then, I attempted to set up a right triangle and solve for the angle but that's where I got confused.
     
  2. jcsd
  3. Sep 14, 2012 #2

    PeterO

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    Homework Helper

    The kayaker will take longer than [30.88] that to cross the harbour, since he/she is not paddling directly towards the opposite side.
     
  4. Sep 14, 2012 #3
    1. The problem statement, all variables and given/known data

    A kayaker needs to paddle north across a 105 m wide harbor. The tide is going out, creating a tidal current that flows to the east at 1.5 m/s. The kayaker can paddle with a speed of 3.4 m/s.

    (a) In which direction should he paddle in order to travel straight across the harbor? (degrees west of north)

    (b) How long will it take him to cross? (seconds)

    Then, I attempted to set up a right triangle and solve for the angle but that's where I got confused.

    -----------------------------------------------------
    Yes you can use a right triangle to solve the problem.
    This is a vector problem and using a right triangle geometry is one of the methods.

    Kayaker speed with direction is one vector.
    The tide speed and direction is another vector.
    You can do operations on this 2 vectors and in this example adding the two vectors.

    The sum of the two vectors will result in the kayaker paddling straight across the habour.
     
  5. Sep 15, 2012 #4
    What azizlwl said.

    If still stuck post your attempt at the vector diagram.
     
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