8-24 할리데이 11판 솔루션 일반물리학

$$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \EE : \text{Electric Energy}\\ \end{cases} $$ $$ \begin{cases} \Delta h&=-120\ut{m}\\ \frac{V}{t}&=1500\ut{m^3/s}\\ \EE&=\frac{3}{4}\KE\\ \rho_{w}&=1000\ut{kg/m^3}\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$\rho=\frac{m}{V},$$ $$ \begin{aligned} \frac{m}{t}&=\rho\cdot\frac{V}{t}\\ &=1000\ut{kg/m^3}\cdot1500\ut{m^3/s}\\ &=1.5\times10^6\ut{kg/s} \end{aligned} $$ $$ \begin{aligned} \Ans&=\frac{\Delta \EE}{t}\\ &=\frac{\Delta (\frac{3}{4}\KE)}{t}\\ &=\frac{ (\frac{3}{4}\Delta\KE)}{t}\\ &=\frac{3\Delta(-\GE)}{4t}\\ &=\frac{3\Delta(-mgh)}{4t}\\ &=\frac{3mg(-\Delta h)}{4t}\\ &=\frac{3}{4}\cdot \frac{m}{t}\cdot g (-\Delta h)\\ &=135g\times10^6\\ &=1323897750\ut{W}\\ &\approx 1.3\times10^9\ut{W}\\ &\approx 1.3\ut{GW}\\ \end{aligned} $$