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Relative Velocity Boat Problem

  1. Sep 20, 2015 #1
    1. The problem statement, all variables and given/known data

    You wish to paddle a boat across an 82 m wide river and land at a boathouse that is 14 m downstream of your starting point. If the current in the river is uniform at 0.50 m/s, how fast and in what direction do you need to row to reach the boathouse in 2.0 minutes?

    2. Relevant equations
    Relative Velocity equation
    VBE = VBW + VWE


    3. The attempt at a solution

    I know that in 2 minutes I would end up 60 m downstream.
    (120 s)(0.50 m/s) = 60 m

    This is 60 - 14 = 46 m away from the boathouse

    Which means that I would need to row upstream at
    46 m / 120 s = .38333 m/s
    And row across the water at a speed of
    82 m / 120 s = .68333 m/s
    to be able to reach my destination in 2 min.

    From this I'm assuming that I can use Pythagorean equation to solve for the resultant vector.
    sqrt[(46m/120s)2 + (82m/120s)2] = .78351061 m/s

    And then the angle of direction through trig
    theta = arctan( (82m/120s) / (46m/120s) ) = 60.7 degrees upstream and across

    I'm not sure if this is right because from the equation I get that
    VWE = 0.50 m/s
     
  2. jcsd
  3. Sep 20, 2015 #2
    I think your answer is correct. But I don't understand your last line :
    "I'm not sure if this is right because from the equation I get that
    VWE = 0.50 m/s"

    And in your relative velocity equation , I don't get what does that "W" represent.
     
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