필요마력 관계식

[출제의도] 지수를 활용하여 문제해결하기 두 비행기 $A$, $B$의 필요마력을 각각 $P _{\mathit{A}}$ , $P _{\mathit{B}}$ 날개의 넓이를 각각 $S _{A}$ , $S _{B}$라 하자. $\displaystyle P _{\mathit{A}} = \frac{1}{150} \mathit{kC} \mathit{\left( V _{A} \right)} ^{3} \mathit{S} _{\mathit{A}}$이고, $S _{B} = 3 S _{A}$이므로 $\displaystyle P _{\mathit{B}} = \frac{1}{150} \mathit{k} \mathit{C} \left( V _{B} \right) ^{3} \mathit{S} _{B} = \frac{1}{150} kC \mathit{\left( \mathit{V} _{B} \right)} ^{3} \left( 3 S _{A} \right)$ $\displaystyle P _{\mathit{B}} = \sqrt{3} P _{\mathit{A}}$이므로 $\displaystyle \frac{P _{A}}{P _{B}} = \frac{1}{\sqrt{3}} = \frac{\left( V _{A} \right) ^{3} S _{A}}{\left( V _{B} \right) ^{3} \left( 3 S _{A} \right)} = \frac{1}{3} \left( \frac{V _{A}}{V _{B}} \right) ^{3}$ $\therefore$ $\displaystyle \left( \frac{V _{\mathit{A}}}{V _{\mathit{B}}} \right) ^{3} = 3 ^{\frac{1}{2}}$ 따라서 $\displaystyle \frac{V _{\mathit{A}}}{V _{\mathit{B}}} = 3 ^{\frac{1}{6}}$