9-46 할리데이 11판 솔루션 일반물리학

$$\begin{cases} m_1&=4.00\ut{kg}\\ \vec v_1&=-4.00\i-5.00\j\ut{m/s}\\ m_2&=6.00\ut{kg}\\ \vec v_2&=6.00\i-2.00\j\ut{m/s}\\ \end{cases}$$ $$\Delta \Sigma \vec p=0,$$ $$m_1v_1+m_2v_2=(m_1+m_2)v_f$$ $$\ab{a}$$ $$\begin{aligned} \vec v_f&=\frac{m_1v_1+m_2v_2}{m_1+m_2}\\ &=2\i-\frac{16}{5}\j\ut{m/s}\\ &=2.00\i-3.20\j\ut{m/s} \end{aligned}$$ $$\ab{b}$$ $$\begin{aligned} v_f&=\sqrt{2^2+\(-\frac{16}{5}\)^2}\\ &=\frac{2\sqrt{89}}{5}\ut{m/s}\\ &\approx 3.7735924528226414\ut{m/s}\\ &\approx 3.77\ut{m/s}\\ \end{aligned}$$ $$\ab{c}$$ $$\begin{aligned} \theta&=\tan^{-1}\frac{-\frac{16}{5}}{2}\\ &\approx -1.0121970114513341\ut{rad}\\ &\approx -1.01\ut{rad}\\ \end{aligned}$$