9-16 할리데이 11판 솔루션 일반물리학

$$\put\begin{cases} 0:\text{Start}\\ 1:\text{After Crash}\\ 2:\text{Landing Ground} \end{cases}$$ $$\put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \end{cases}$$ $$\begin{cases} m_A&=3.2\ut{kg}\\ m_B&=2.0\ut{kg}\\ h&=0.30\ut{m}\\ v_{0}&=3.0\ut{m/s} \end{cases}$$ $$\put M = m_A+m_B=5.2\ut{kg}$$ $$\Delta \Sigma \vec P=0,$$ $$m_Av_{A0}=Mv_1,$$ $$\begin{aligned} v_1&=\frac{m_A}{M}v_0 \end{aligned}$$ $$\Sigma \Delta E=0,$$ $$\Delta \KE+\Delta \GE=0$$ $$\begin{aligned} \KE_2&=\KE_1-\Delta \GE\\ &=\frac{1}{2}M{v_1}^2+Mg(-\Delta y)\\ &=\frac{1}{2}M\(\frac{m_Av_0}{M}\)^2+Mgh\\ &=\frac{(m_Av_0)^2}{2M}+Mgh\\ &=\frac{39 g}{25}+\frac{576}{65}\\ &\approx 24.15991246153846\ut{J}\\ &\approx 24\ut{J}\\ \end{aligned}$$