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Homework Help: Multivariable calc, boat moving on river functions problem

  1. Feb 21, 2012 #1
    1. The problem statement, all variables and given/known data
    there is a straight river 40m wide.
    the water speed on the river can be expressed as the function f(x)=3sin(∏x/40)
    If a boat is to cross the river from point a to point b at a constant velocity of 5 m/s determine the angle the boater should head.

    2. Relevant equations

    3. The attempt at a solution
    it will take 8 seconds for the boater to cross the river.
    I am thinking that since I am given that the river is 40m wide,
    that I should integrate f(x) to find the distance the boater will have traveled after 8 seconds. then take the inverse tangent of (40/(∫f(x)|0->8?) to find the angle?
  2. jcsd
  3. Feb 22, 2012 #2


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    hi mike1967! :wink:
    no it won't :redface:

    start again! :smile:
  4. Feb 22, 2012 #3
    I'm not sure where to start then. I figured t=8 because v(t)=5 to x(t)=5t 40=5t 8=t.
  5. Feb 22, 2012 #4


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    start by calling the angle "θ",

    then find t from the x-component equation :smile:
  6. Feb 22, 2012 #5
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