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If the boat is driven by the current then there's no force relative to the stream. I would stick to velocities.
Today while solving a boat / river problem, I wasn't convinced of vector drawing to find velocities. I was thinking of force acting on the boat which affects its position and velocity. But I couldn't think clearly of FORCE equation to find displacement, accelerations etc. Please help me. Assume river velocity : VR, Boat still water velocity : VB, Distance from Point A to B = D (straight distance from bank to bank). Now please explain how to find position of the boat in the form r = f(Ө) .