Question

The force required to row a boat at constant velocity is proportional to square of its speed. If a speed v km/h requires 4 kW, how much power does a speed of 2v km/h require?

• A. $32KW$
• B. $8KW$
• C. $24KW$
• D. $16KW$

Answer 1

The correct option is A $32KW$

$\begin{array}{c}F\alpha V^2\\ P=F\times V\\ \alpha V^2\times V=V^3\\ \frac{P_1}{P_2}=\frac{{V_1}^3}{{V_2}^3}={\left(\frac{V}{2V}\right)}^3=\frac{1}{8}\\ P_1=4KW\\ P_2=8\times 4=32KW\end{array}$

Hence,

option $\left(A\right)$ is correct answer.