Power of Boat: Exploring R vs F

[Faiq]

Homework Statement

A boat moving at constant speed v through still water experiences a total frictional drag F.
What is the power developed by the boat?
a) 1/2Fv b) Fv

The Attempt at a Solution

I know the correct answer is b. My confusion is why is a incorrect?
My reasoning: The boat experiences a total drag of F. Which means at every point the boat experiences a resistance where R < F. Thus to steer at v, we have to apply a force of R. Which will provide the only option 1/2Fv.

 

[Delta2]

What exactly happens at every point between the boat and the water is a big story of fluid dynamics I doubt we want to discuss for this specific problem. There will be an infinitesimal force $dF_i$ at every point and the sum(more accurately the integral) of all these forces will be $\vec{F}+\vec{A}=\sum \vec{dF_i}$ , where A is the buoyancy force which is canceled by the weight of the boat. So all that is left is the force F. So we have to supply a force equal and opposite to F to keep the boat move at constant speed v. If you do the math (starting from the definition of the power and also using the definition of work of a force) for a constant force applied at a body that moves with constant velocity v, the power provided by force F is equal to Fv.

 

[rude man]

I know the correct answer is b. My confusion is why is a incorrect?
My reasoning: The boat experiences a total drag of F. Which means at every point the boat experiences a resistance where R = F. Thus to steer at v, we have to apply a force of R. Which will provide the only option 1/2Fv.

Drag and resistance are the same thing!