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Homework Help: Relative velocity

  1. Apr 26, 2010 #1
    1. The problem statement, all variables and given/known data
    Man can swim 3m/s in the water, water flows 5m/s. River is 176 m wide Find direction at which a) he will end up as little downstream as possible, b) as quick as possible.


    2. The attempt at a solution

    For b) I think it would be the fastest speed possible i.e. 90 degrees towards bank.
    u_r = 5i +0j
    u_m = 0i+3j
    vm/r = 5i - 3j = 5.83 m/s, which seems to me give the fastest time of 30 seconds.

    For a) I'm not too sure, I though the angle would be 45 degrees up stream but than when I work out everything, distance in downstream would be over 200, where in the case of b) downstream was only 170.

    Thanks for any hi
     
  2. jcsd
  3. Apr 27, 2010 #2

    HallsofIvy

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    Draw a picture. Draw an arrow pointing upward at angle [math]\theta[/math] having length 3t, where t is the time to swim across, to the other bank, then an arrow pointing directly downstream having length 5t m/s . To go "end up downstream as little as possible", the least possible would be no downstream at all which is why I said "to the other bank".

    We now have a right triangle with legs of length 3t and 5t and hypotenuse 176 m. The angle upstream is given by [itex]tan(\theta)= \frac{5t}{3t}= \frac{5}{3}[/itex]
     
  4. Apr 27, 2010 #3
    But this would look like this

    attachment.php?attachmentid=25415&d=1272368349.jpg

    Which makes an angle of θ = Sin^-1 5/3, which is impossible.

    Why do you take is as Tan θ
     

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