9-36 할리데이 11판 솔루션 일반물리학

$$\begin{cases} m_\alpha&=4.00\ut{u}\\ m_{\text{O}}&=16.0\ut{u}\\ \theta_\alpha&=-64.0\degree\\ v_{\text{O}f}&=1.20\times10^5\ut{m/s}\\ \theta_{\text{O}}&=40.0\degree\\ \end{cases}$$ $$\Delta \Sigma \vec p=0,$$ $$\begin{cases} p_{xi}&=\Sigma p_{xf}\\ 0&=\Sigma p_{yf}\\ \end{cases}$$ $$\begin{cases} m_\alpha v_{\alpha i}&=m_\alpha v_{\alpha x f}+m_{\text{O}} v_{\text{O} x f}\\ 0&=m_\alpha v_{\alpha y f}+m_{\text{O}} v_{\text{O} y f}\\ \end{cases}$$ $$\begin{cases} m_\alpha v_{\alpha i}&=m_\alpha v_{\alpha f}\cos\theta_\alpha+m_{\text{O}} v_{\text{O} f}\cos\theta_{\text{O}}\\ 0&=m_\alpha v_{\alpha f}\sin\theta_\alpha+m_{\text{O}} v_{\text{O} f}\sin\theta_{\text{O}}\\ \end{cases}$$ $$\begin{cases} v_{\alpha i}&= -\cfrac{m_\text{O}}{m_\alpha}\cdot \cfrac{\sin\(\theta_\text{O}-\theta_\alpha\)}{\sin \theta_\alpha}\cdot v_{\text{O}f}\\ v_{\alpha f}&= -\cfrac{m_\text{O}}{m_\alpha}\cdot\cfrac{\sin \theta_\text{O}}{\sin\theta_\alpha}\cdot v_{\text{O}f} \end{cases}$$ $$\ab{a,b}$$ $$\begin{cases} v_{\alpha i}&= 4.8\cdot\cfrac{\cos14\degree}{\cos26\degree}\times10^5\ut{m/s}\\ v_{\alpha f}&= 4.8\cdot\cfrac{\sin40\degree}{\cos26\degree}\times10^5\ut{m/s}\\ \end{cases}$$ $$\begin{cases} v_{\alpha i}&\approx 5.181853957869391\times10^5\ut{m/s}\\ v_{\alpha f}&\approx 3.432800360883129\times10^5\ut{m/s}\\ \end{cases}$$ $$\begin{cases} v_{\alpha i}&\approx 5.18\times10^5\ut{m/s}\\ v_{\alpha f}&\approx 3.43\times10^5\ut{m/s}\\ \end{cases}$$ $$\begin{cases} v_{\alpha i}&\approx 518\ut{km/s}\\ v_{\alpha f}&\approx 343\ut{km/s}\\ \end{cases}$$