Work, Energy and Power: Question 4

Worked solution

Step 1: Recall the relationship between power, force and velocity

For a force $F$ moving an object at a steady velocity $v$ in the direction of the force, the power delivered is: $P = Fv$

Step 2: Identify the correct force to use

Since the speedboat moves at constant velocity, its acceleration is zero, so by Newton’s first law the resultant force on it must be zero. This means the engine’s driving force is exactly equal in magnitude to the total resistive force: $F_{\text{drive}} = F_{\text{resistive}} = 3600\text{ N}$

Step 3: Substitute the values

$P = Fv = 3600\times12$

Working this as $3600\times12 = 3600\times10+3600\times2=36000+7200=43200\text{ W}$.

Check by recomputing differently: $3600\times12=(3600\times4)\times3=14400\times3=43200\text{ W}$. Both routes agree.

Why the other options are wrong

• A ($300\text{ W}$): this comes from dividing the force by the velocity ($3600/12$) instead of multiplying them.
• B ($3612\text{ W}$): this comes from adding the numerical values of the force and velocity ($3600+12$), which is dimensionally meaningless.
• C ($21600\text{ W}$): this comes from inserting an extra factor of $\tfrac12$, as if using the kinetic energy formula $\tfrac12mv^2$, giving half the correct power.

Final answer

• The useful output power of the boat’s engine is $\boxed{43200}\text{ W}$, option D.