솔루션피아

$$\put \begin{cases} m:\text{man}\\c:\text{car}\\\end{cases} $$$$ \begin{cases} m_mg&=850\ut{N}\\m_cg&=1700\ut{N}\\v_{ci}&=18.2\ut{m/s}\\v_{m\larr c}&=-4.00\ut{m/s}\end{cases} $$$$ \begin{aligned}v_{m\larr c}&=v_m-v_c\end{aligned} $$$$\Delta \Sigma \vec p=0,$$$$\vec p_i=\vec p_{mf}+\vec p_{cf}$$$$(m_m+m_c)v_i=m_mv_m+m_cv_c$$$$ v_c=v_i-\frac{m_m }{m_c+m_m}v_{m\larr c}$$$$ \begin{aligned}\Delta v_..

$$ \begin{cases} x_P&=0\\x_Q&=1.0\ut{m}\\m_P&=0.10\ut{kg}\\m_Q&=0.30\ut{kg}\\F&=1.0\times10^{-2}\ut{N}\\\end{cases} $$$$\ab{a}$$$$\Delta \Sigma \vec p=0,$$$$\vec p_{\com i}=\vec p_{\com f},$$$$\vec v_{\com i}=\vec v_{\com f}=0$$$$\ab{b}$$$$ \begin{aligned}x_{\text{crash}}&=x_\com\\&=\frac{\Sigma xm}{M}\\&=\frac{x_Pm_P+x_Qm_Q}{m_P+m_Q}\\&=\frac{3}{4}\ut{m}\\&=0.75\ut{m}\end{aligned} $$

$$ \put \begin{cases} m:\text{Mother}\\d:\text{Daughter}\\n:\text{neutrino}\\e:\text{electron}\\\end{cases} $$$$ \begin{cases} p_m&=0\\p_e&=-1.2\times10^{-22}\i\ut{kg\cdot m/s}\\p_n&=-6.4\times10^{-23}\j\ut{kg\cdot m/s}\\m_d&=5.8\times10^{-26}\ut{kg}\\\end{cases} $$$$ \begin{aligned}\vec p_m&= \vec p_d+ \vec p_e+ \vec p_n\\\vec p_d&=-\vec p_e- \vec p_n\\&=1.2\times10^{-22}\i+6.4\times10^{-23}\j\..

$$ \put \begin{cases} \KE : \text{Kinetic Energy}\\\end{cases} $$$$ \begin{cases} m&=150\ut{g}\\v_i&=5.2\ut{m/s}\\\KE_f&=\frac{1}{2}\KE_i\end{cases} $$$$\ab{a}$$$$ \begin{aligned}\KE_f&=\frac{1}{2}\KE_i\\\frac{1}{2}m{v_f}^2&=\frac{1}{2}\cdot\frac{1}{2}m{v_i}^2\\\end{aligned} $$$$ \begin{aligned}v_f&=\sqrt\frac{1}{2}\cdot{v_i}\\&=\frac{v_i}{\sqrt2}\\&=\frac{13\sqrt2}{5}\ut{m/s}\..

$$\put \begin{cases} r:\text{red}\\b:\text{blue}\end{cases} $$$$ \begin{cases} v_i&=4.00\ut{m/s}\\\theta&=40.0\degree\\\end{cases} $$$$ \begin{cases} v_{ri}&=v_i\cos\theta\i+v_i\sin\theta\j\\v_{bi}&=v_i\cos\theta\i-v_i\sin\theta\j\\\end{cases} $$$$ \Delta p_x = 0, $$$$ \begin{cases} p_{rix}=p_{rfx}\\p_{bix}=p_{bfx}\\\end{cases} $$$$ \put \begin{cases} v_{\text{in}}&=\vec v_{..

$$ \begin{cases} v_{1i}&=10\ut{m/s} \end{cases} $$ $$ \begin{cases} \theta_1&=0\\ \theta_2&=+30\degree\\ \theta_3&=-30\degree\\ \end{cases} $$ $$\because \triangle 123=\text{Equilateral Triangle}$$ $$\Delta \Sigma \vec p=0,$$ $$ \begin{aligned} \vec p_{1i}&=\vec p_{1f}+\vec p_{2f}+\vec p_{3f}\\ m\vec v_{1i}&=m\vec v_{1f}+m\vec v_{2f}+m\vec v_{3f}\\ \vec v_{1i}&=\vec v_{1f}+\vec v_{2f}+\vec v_{3f..

$$ \put \begin{cases} 0:\text{Start}\\ 1:\text{After Turn}\\ 2:\text{Stop} \end{cases} $$ $$ \begin{cases} m&=1400\ut{kg}\\ v_0&=5.3\ut{m/s}\\ \vec v_0&=v_0\j\\ \Delta t_{0\rarr1} &= 4.6\ut{s}\\ \vec v_1&=v_0\i\\ \Delta t_{1\rarr2} &= 350\ut{ms}=0.35\ut{s}\\ \vec v_2&=0 \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} \vec J_{0\rarr1} &=\Delta \vec p_{0\rarr1}\\ &=\vec p_1-\vec p_0\\ &=m v_0\i-m v_0..

$$ \begin{cases} m_L&=1.00\ut{kg}\\ m_R&=0.500\ut{kg}\\ \end{cases} $$ $$\Delta \Sigma \vec p=0,$$ $$m_Lv_L+m_Rv_R=0$$ $$\ab{a}$$ $$v_L=-1.20\ut{m/s},$$ $$ \begin{aligned} v_R&=-\frac{m_L}{m_R}v_L\\ &=\frac{12}{5}\ut{m/s} \end{aligned} $$ $$ \begin{aligned} S&=vt\\ &=\frac{48}{25}\ut{m}\\ &=1.92\ut{m} \end{aligned} $$ $$\ab{b}$$ $$v_{L\larr R}=-1.20\ut{m/s},$$ $$ \begin{cases} m_Lv_L+m_Rv_R=0\\ ..

$$ \begin{cases} m_\alpha&=4.00\ut{u}\\ m_{\text{O}}&=16.0\ut{u}\\ \theta_\alpha&=-64.0\degree\\ v_{\text{O}f}&=1.20\times10^5\ut{m/s}\\ \theta_{\text{O}}&=40.0\degree\\ \end{cases} $$ $$\Delta \Sigma \vec p=0,$$ $$ \begin{cases} p_{xi}&=\Sigma p_{xf}\\ 0&=\Sigma p_{yf}\\ \end{cases} $$ $$ \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_..

$$ \begin{cases} \vec r(t\ut{s})&=(3500-160t)\i+2700\j+300\k\ut{m}\\ m&=250\ut{kg} \end{cases} $$ $$ \begin{aligned} \vec v&=\dyt{\vec r}\\ &=-160\i\ut{m/s} \end{aligned} $$ $$\ab{a}$$ $$ \begin{aligned} \vec p&=m\vec v\\ &=-40000\i\ut{kg\cdot m/s}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} \vec v&=-160\i\ut{m/s}, \end{aligned} $$ $$\text{West}$$ $$\ab{c}$$ $$ \begin{aligned} \vec F&=m\vec..