1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: A Swimmer's Problem

  1. Aug 30, 2012 #1
    I found an answer, but I am skeptical.

    What must the swimmer's speed, vs, be in order that he drifts only 1 mile downstream as he crosses the river?

    The width of the river = 2 miles
    The velocity of the river, vr = 3(1-x^2)

    Relevant equations:

    dy/dx = tanα
    vr = v0(1-x^2/a^2)


    So I started off with:

    plugged in dy/dx for tanα, and vr = 3(1-x^2)

    dy/dx = (3/vs)(1-x^2)
    I assumed that vs was a constant.
    ∫dy/dx = (3/vs)∫(1-x^2)dx

    y = (3/vs)(x - 1/3 x^3) + C

    plugged in initial values y(-1) = 0,

    0 = (3/vs)((-1) - 1/3(-1)^3) + C
    ((-1) - 1/3(-1)^3) = -2/3
    0 = (3/vs)(-2/3) + C
    C = 2/vs

    now I have the equation all with 1 unknown:

    y = (3/vs)(x - 1/3 x^3) + 2/vs

    here is the part where I just improvised not really knowing what to do...
    I figured that if I used the initial values, I wouldn't get my vs, so I used the final values:

    1 = (3/vs)(1 - 1/3) + 2/vs
    and for this one I get that:
    vs = 4 mi/h
  2. jcsd
  3. Aug 30, 2012 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Looks OK to me. The ##a## in the picture is evidently 1.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook