8-69 할리데이 11판 솔루션 일반물리학

$$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \TE : \text{Thermal Energy}\\ \ME : \text{Mechanical Energy}\\ \end{cases} $$ $$ \begin{cases} m&=8.10\ut{kg}\\ \Delta \ME&=-72.0\ut{kJ}=-72000\ut{J}\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$\Delta \TE=-\Delta \ME,$$ $$\Sigma \Delta E=\Delta \KE_1+\Delta \GE_1+\Delta \TE_1=0,$$ $$ \begin{aligned} \Delta \GE_1&=-\Delta \KE_1-\Delta \TE_1\\ &=(\KE_i-\KE_f)-\Delta \TE_1\\ &=\KE_i+\Delta \ME_1\taag1\\ \end{aligned} $$ $$\Sigma \Delta E=\Delta \KE_2+\Delta \GE_2=0,$$ $$ \begin{aligned} \Delta \GE_2&=-\Delta \KE_2\\ &=(\KE_i-\KE_f)\\ &=\KE_i\taag2\\ \end{aligned} $$ $$ \begin{aligned} \Ans&=\Delta y_2-\Delta y_1,\\ mg\Ans&=\Delta mgy_2-\Delta mgy_1\\ &=\Delta\GE_2-\Delta\GE_1\\ &=(\KE_i)-(\KE_i+\Delta \ME_1)\\ &=-\Delta \ME_1\\ \end{aligned} $$ $$ \begin{aligned} \Ans&=\frac{-\Delta \ME_1}{mg}\\ &=\frac{80~000}{9g}\\ &\approx 906.4144115359362\ut{m}\\ &\approx 906\ut{m}\\ \end{aligned} $$