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A ship going upstream and experiences a frictional force

  1. Nov 16, 2006 #1
    Hello there!

    This problem is giving me a hard time and I thought maybe one of you could give me a hint:

    "A ship is going upstream with a constant power P. Its speed [tex]V[/tex] is relative to the water and the water's speed [tex]U[/tex] is relative to the shore. The ship needs tp overcome a frictional force of [tex]F_r=cv^2[/tex] caused by the water which depends on its relativ speed. How big does v have to be so that the ship goes from A to B with the lowest energy consumption?"

    Where I would start is that the ship needs at least the power which is neccesary to stay in the same place. Which would be
    [tex] P=F_r x U = cU^2U=cU^3[/tex] and than in addition some extra power to go upstream. That would be [tex] P=F_r x (v-u)=c(V-U)^2 x (V-U)[/tex]. But from here, if it's really correct, I do not know how to continue :(
  2. jcsd
  3. Nov 16, 2006 #2


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    Science Advisor

    I assume the "x" in your formula is a multiplication sign. Don't do that, it's confusing. Just [itex]P= F_rU[/itex] would be sufficient.
    I don't believe you can or should distinguish between the power necessary to "stand still" and the power necessary to move forward against the current. They are the same. Note also that U is speed of the boat relative to the water so it makes no sense to use V-U (which would be negative: if the boat is moving forward against the current, U> V).
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