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Relative velocity of river flowing

  1. Feb 16, 2013 #1
    1. The problem statement, all variables and given/known data

    A 400m wide river flows from west to east at 30 m/min. Your boat moves at 100m.min relative to the water no matter which direction you point. To cross the river, you start from a dock at point A on the south bank. There is a boat landing directly opposite at point B on the north bank, and also one at point C, 75m downstream from B.


    (a) Where on the north shore will you land if you point your boat perpendicular to the water current, and what distance will you have traveled?

    (b)If you initially aim your boat directly toward point C and do not change the bearing relative to the shore, where on the north shore will you land?

    (c) To reach point C:(i)at what bearing must you aim you boat, (ii) how long will it take to cross the river, (iii) what distance do you travel, and (iv) what is the speed of your boat as measured by an observer standing on the river bank?

    [url=http://www.freeimagehosting.net/zvsuk][PLAIN]http://www.freeimagehosting.net/t/zvsuk.jpg[/url][/PLAIN]

    2. Relevant equations
    Vb/w= velocity of boat relative to water
    Vw/e= velocity of water realtive to earth
    Vb/e= velocity of boat relative to earth.

    Vb/w=100m/min=1.66m/s
    Vw/e= 30m/mon=0.5m/s

    V=D/T


    3. The attempt at a solution

    A:
    Vb/w=Dy/T

    1.67m/s=400m/T
    T=240 seconds

    Vw/e=Dx/T
    0.5m/s=Dx/240seconds
    Dx=120m from B

    B: This is where I am stuck. I do not understand the question.It says to keep my bearing relative to the shore and I am not sure what that means.
    Thanks in advance!
     
  2. jcsd
  3. Feb 16, 2013 #2

    haruspex

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    It means you keep the boat's angle to the shore the same. It's just the same as the first part, but with a different fixed velocity of boat relative to water.
     
  4. Feb 17, 2013 #3
    the south shore?
     
  5. Feb 17, 2013 #4
    Is it this angle?

    [url=http://www.freeimagehosting.net/2e923][PLAIN]http://www.freeimagehosting.net/t/2e923.jpg[/url][/PLAIN]
     
  6. Feb 18, 2013 #5

    haruspex

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    Yes, that's the bearing. But not, of course, the path the boat will take.
     
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