Topic: Automobile Engineering
An automobile moving at a velocity of 40 $km/hr$ is experiencing a wind resistance of 2kN. If the automobile is moving at a velocity of 50 $km/hr$, the power required to overcome the wind resistance is-
- A. 43.4kW
- B. 3.125kW
- C. 2.5kW
- D. 27.776kW
Answer: A. 43.4kW
Explanation: Given $F_{1} = 2~kN$, $V_{1} = 40~km/hr$, $V_{2} = 50~km/hr$. Wind resistance force $F = \rho A V^{2}$ (thus $F \propto V^{2}$). $\frac{F_{1}}{V_{1}^{2}} = \frac{F_{2}}{V_{2}^{2}} \Rightarrow F_{2} = F_{1} \times (\frac{V_{2}}{V_{1}})^{2} = 2 \times (\frac{50}{40})^{2} = 2 \times \frac{25}{16} = 3.125~kN$. Power required to overcome is $P = F_{2} \times V_{2} = \frac{3.125 \times 1000 \times 50 \times (5/18)}{1000} kW \approx 43.4~kW$.