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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 :(

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# A ship going upstream and experiences a frictional force

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