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Homework Help: Relative Velocity of two swimmers

  1. Aug 29, 2007 #1
    1. The problem statement, all variables and given/known data


    Two swimmers, Alan and Beth, start together at the same point on the
    bank of a wide stream that flows with a speed v. Both move at the
    same speed c (c > v), relative to the water. Alan swims downstream a
    distance L and then upstream the same distance. Beth swims so that her
    motion relative to the Earth is perpendicular to the banks of the stream.
    She swims the distance L and then back the same distance, so that both
    swimmers return to the starting point. Which swimmer returns first?
    (Note: First guess the answer.)


    2. Relevant equations

    relative velocity and vector


    3. The attempt at a solution

    let time taken for Alan swim for a distance Ta= L / (V+C)

    let time taken for Beth swim for a distance Tb= L / [tex]\sqrt{}[/tex]c[tex]^{}2[/tex]+v[tex]^{}2[/tex]

    compare this 2 equation, its obvious Alan will took the less time to finish a distance, L. but the question ask distance of 2L. so i am not sure the vector calculation for Beth to swim back to the origin point.

    hope someone can help me out.this is my 1st year physics tutorial question.thanks :eek:
     
    Last edited: Aug 29, 2007
  2. jcsd
  3. Aug 29, 2007 #2
    you forgot to take in account the return distance?
    because they returned back to the same place.

    it's from Irodov lol
     
    Last edited: Aug 29, 2007
  4. Aug 29, 2007 #3
    i aware of the return distance which i mention it as 2L.
    nonetheless, thank for the tip for Irodov. shall take a look at it carefully.thanks again
     
  5. Aug 30, 2007 #4
    Ta= L / (V+C) + L / (V-C)
    Tb=2*L/[tex]\sqrt{}[/tex]c[tex]^{}2[/tex]+v[tex]^{}2[/tex]
     
  6. Aug 30, 2007 #5

    yupe, i got it.thanks :D
     
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