9-22 할리데이 11판 솔루션 일반물리학

$$ \put \begin{cases} 0:\text{Start}\\ 1:\text{After Crash}\\ 2:\text{Highest Point} \end{cases} $$ $$ \begin{cases} m_A&=3.0\ut{kg}\\ v_{A0}&=28\ut{m/s}\\ m_B&=2.0\ut{kg}\\ v_{B0}&=-12\ut{m/s}\\ M&=m_A+m_B=5\ut{kg}\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \end{cases} $$ $$\Delta \Sigma \vec P=0,$$ $$ \begin{aligned} Mv_1&=m_Av_{A0}+m_Bv_{B0}\\ v_1&=\frac{m_Av_{A0}+m_Bv_{B0}}{M}\\ &=12\ut{m/s} \end{aligned} $$ $$\Sigma \Delta E=0,$$ $$ \begin{aligned} \Delta \GE&=-\Delta \KE\\ mg\Delta h&=-\frac{1}{2}m\Delta(v^2)\\ \end{aligned} $$ $$ \begin{aligned} h_2&=\frac{{v_1}^2-{v_2}^2}{2g}\\ &=\frac{{v_1}^2}{2g}\\ &=\frac{72}{g}\\ &\approx 7.341956733441084\ut{m}\\ &\approx 7.3\ut{m}\\ \end{aligned} $$