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Rowing across a river

  1. Jan 15, 2014 #1
    1. The problem statement, all variables and given/known data

    You wish to row straight across a 63m wide river. You can row at a steady 1.3 m/s relative to the water, and the river flows at 5.7 m/s. In what direction should you head? How long will it take you to cross the river?

    3. The attempt at a solution

    Capture.JPG

    Is the answer right? Could the answer equally be 26°?
     
    Last edited: Jan 15, 2014
  2. jcsd
  3. Jan 15, 2014 #2

    phinds

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    Think about this with simple logic for a minute. The river is flowing downstream at some speed. In order to not be at all swept downstream, the upstream component of your rowing speed relative to the river has to exactly match the downstream speed of the river. Is that possible in this problem?
     
  4. Jan 15, 2014 #3
    I suppose the answer is 116° instead of 64°.
     
  5. Jan 15, 2014 #4

    phinds

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    Are you going to answer my question or just continue to ignore it?
     
  6. Jan 15, 2014 #5
    I've already answered it. In rowing at 116° from the x-axis, the boat goes against the current, no?
     
  7. Jan 15, 2014 #6
    I tried solving it from another approach, where;

    (1.3ms^-1)^2 = (0.57ms^-1)^2 +y^2
    y = 1.168ms^-1
    theta = 26°
     
  8. Jan 15, 2014 #7

    phinds

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    You need to reread my question in post #2. You have not answered it.
     
  9. Jan 15, 2014 #8

    haruspex

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    There's a typo in the OP. If you look at the attachment you'll see the river speed is given as 0.57 m/s.
    Yes, negation, the answer is 26 degrees to the normal.
     
  10. Jan 15, 2014 #9

    phinds

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    Ah ... well that explains it.
     
  11. Jan 15, 2014 #10

    My mistake for the typo. I apologize.
    Would that be the same as 116 degrees from the x-axis since it would in other words implies 26 degrees NW.

    Edit: I think it is.
     
  12. Jan 15, 2014 #11

    It's not possible since
    v_downwards> v_upwards.
    I made a typo in the values.
     
  13. Jan 15, 2014 #12

    haruspex

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    Since the OP says nothing about x or y axes, nor about compass directions, that's impossible to answer.
    In terms of river bank and direction of flow of river, where were you measuring 116 degrees from?
     
  14. Jan 15, 2014 #13
    I measured 116° from the x-axis.
    That would put the boat in quadrant 2 but of course since there was no reference point mentioned by the question, it could equally be implied 26° NW, 64° from the x-axis or 26° NE, isn't it?
    I have a preference for 116° from the x-axis to do away with all the bearings.
     
  15. Jan 15, 2014 #14

    haruspex

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    I cannot see inside your head. I do not know where your x axis is, nor which way the river runs in terms of a compass bearing.
     
  16. Jan 15, 2014 #15
    Untitled.jpg

    There.
     
  17. Jan 16, 2014 #16

    haruspex

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  18. Oct 27, 2015 #17
    How long will it take?
    t=d/v
    t=63/1.3=48.5 s
    is it correct?
    i am comfused since the answer in my textbook tells that t=53.9 s.
    please, provide me with explanation.
    Regards.
     
  19. Oct 27, 2015 #18

    haruspex

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    The 1.3m/s is the rowing speed relative to the water. It would take 48.5 s if you were to head straight across, relative to the water. But then you would end up somewhat downstream when you landed. In order to row straight across relative to the riverbank, you have to aim a little upstream. That means some of your 1.3m/s is spent countering the flow of the water.
     
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