Question 27: A boat moving at constant speed v through still water experiences total frictional drag F. What is the power developed by the boat? (Work, Power & Energy, power and energy)

Explanation

Correct Answer: (d) Fv Explanation:Power is the rate of work done, and work is defined as the product of force and displacement in the direction of that force.Here, the frictional drag force (F) acts against the boat's motion, but the boat maintains a constant speed. This means there is no displacement in the direction of the drag force, making the work done zero (W=F.0=0)However, the engine is still expending power to counteract the drag force, and this power can be calculated by =W/t=tF⋅0 =Fv. Therefore, the engine continuously delivers Fv power to maintain the constant speed.Incorrect Answers:(a) Fv/2 : This underestimates the power required. While it considers the force and speed, dividing by 2 is not justified in this case. The work done against the drag force directly translates to the engine's power output, and dividing by 2 introduces an unnecessary factor.(b) F v^2/2 : This relates to the kinetic energy of a moving object, which is not relevant in this scenario. The boat maintains a constant speed, not accelerating or gaining kinetic energy. This option confuses the concept of power (rate of work) with kinetic energy (total energy stored in motion).(c)Fv^2: Similar to option (b), this overestimates the power required. Squaring the velocity introduces an additional factor unrelated to the work done against the drag force. The engine's power output is directly proportional to the force it overcomes, not the square of the boat's speed.