솔루션피아

$$ \begin{cases} m_1&=16.7\times10^{-27}\ut{kg}\\ m_2&=8.35\times10^{-27}\ut{kg}\\ m_3&=11.7\times10^{-27}\ut{kg}\\ \vec v_1&=+6.00\times10^6\i\ut{m/s}\\ \vec v_2&=-8.00\times10^6\j\ut{m/s}\\ \end{cases} $$ $$\ab{a}$$ $$\Delta \Sigma \vec P=0,$$ $$ \vec P_i=\Sigma \vec P_f $$ $$ 0=m_1\vec v_1+m_2\vec v_2+m_3\vec v_3 $$ $$ \begin{aligned} \vec v_3&=\frac{-m_1\vec v_1-m_2\vec v_2}{m_3}\\ &=-\frac{..

$$ \put\begin{cases} A:\text{3d x 3d Box}\\ B:\text{2d x 2d Box}\\ C:\text{A-B Box} \end{cases} $$ $$ \begin{cases} 6d&=6.0\ut{m}\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{cases} x_{\com A} &=0\\ x_{\com B}&=2d\\ \end{cases} $$ $$\vec r_{\com} = \frac{\Sigma m\vec r}{M}= \frac{\Sigma V\vec r}{V_s},$$ $$ \begin{aligned} x_{\com A}&= \frac{\Sigma V\vec r}{V_A}\\ &=\frac{V_Bx_{\com B}+V_Cx_{\com C}}{V_..

$$ \begin{cases} p_0&=8.0\ut{kg\cdot m/s}\\ p_1&=4.0\ut{kg\cdot m/s}\\ \end{cases} $$ $$ \begin{aligned} \vec p_0&=8\cos\theta\i+8\sin\theta\j\\ \vec p_1&=8\cos\theta\i=4\i \end{aligned} $$ $$ \begin{aligned} \theta&=\cos^{-1}\frac{4}{8}\\ &=\frac{\pi}{3}\ut{rad}\\ &\approx 1.0471975511965976\ut{rad}\\ &\approx 1.0\ut{rad}\\ \end{aligned} $$

$$ \begin{cases} m&=4.0\ut{g}=4.0\times10^{-3}\ut{kg}\\ f&=120\ut{/min}\\ \vec v_i&=500\ut{m/s}\\ \vec v_f&=-\vec v_i=-500\ut{m/s}\\ \end{cases} $$ $$ \begin{aligned} T&=\frac{1}{f}\\ &=\frac{1\ut{min}}{120}\\ &=\frac{1}{2}\ut{s} \end{aligned} $$ $$\vec J=\Delta \vec P,$$ $$F\Delta t=m\Delta \vec v$$ $$ \begin{aligned} \vec F&=\frac{m(\vec v_f-\vec v_i)}{T}\\ &=-\frac{2m\vec v_i}{T}\\ &=-8\ut{N}..

$$ \begin{cases} m_A&=500.0\ut{kg}\\ m_B&=400.0\ut{kg}\\ M&=m_A+m_B\\ \end{cases} $$ $$ \begin{cases} v_{i}&=1000\ut{m/s}\\ v&=v_{A\larr Bf}=-100.0\ut{m/s} \end{cases} $$ $$\Delta \Sigma \vec P=0,$$ $$ \begin{cases} Mv_i&=m_Av_{Af}+m_Bv_{Bf}\\ v_{A\larr Bf}&=v_{Af}-v_{Bf}\\ \end{cases} $$ $$ \begin{cases} v_{Af}&=v_i+\cfrac{m_B}{M}v\\ v_{Bf}&=v_i-\cfrac{m_A}{M}v\\ \end{cases} $$ $$ \begin{cases}..

$$ \put\begin{cases} i:\text{Start}\\ j:\text{After A B Crash}\\ k:\text{After Wall Crash}\\ \end{cases} $$ $$ \begin{cases} m_1&=6.6\ut{kg}\\ v_{1k}&=v_{1j}\\ v_{2k}&=-v_{2j}\\ v_{1k}&=v_{2k}=v_k\\ \end{cases} $$ $$ \text{Elastic Collision}\Harr\vec v_{\text{in}}+ \vec v_{\text{out}}=0,$$ $$ \begin{aligned} v_{1i}+v_{1j}&=v_{2i}+v_{2j}\\ 0+v_{1k}&=v_{2i}-v_{2k}\\ v_{k}&=v_{2i}-v_{k}\\ v_{2i}&=2..

$$ \begin{cases} m&=2900\ut{kg}\\ v&=175\ut{m/s}\\ \Delta m&=920\ut{kg}\\ \end{cases} $$ $$\Delta \Sigma \vec P=0,$$ $$ \begin{aligned} m_iv_i&=m_fv_f\\ v_f&=\frac{m_i}{m_f}v_i\\ &=\frac{25375}{191}\ut{m/s}\\ &\approx 132.85340314136127\ut{m/s}\\ &\approx 133\ut{m/s}\\ &\approx 1.3\times10^2\ut{m/s}\\ \end{aligned} $$

$$ \begin{cases} \vec v_0&=v_0\i\\ v_{A1}&=3.50\ut{m/s}, \theta_{A1}&=22.0\degree\\ v_{B1}&=2.00\ut{m/s} \end{cases} $$ $$ \begin{cases} \vec v_{A1}&=3.5\cos22\degree\i+3.5\sin22\degree\j\\ \vec v_{B1}&=2\cos\theta\i+2\sin\theta\j\\ \end{cases} $$ $$\Delta \Sigma \vec P=0,$$ $$ \begin{aligned} \vec P_0&=\vec P_{A1}+\vec P_{B1}\\ m\vec v_0&=m\vec v_{A1}+m\vec v_{B1}\\ \vec v_0&=\vec v_{A1}+\vec v..

$$ \begin{cases} m_A&=2140\ut{kg}\\ m_B&=242\ut{kg}\\ v_{Ai}&=0\\ v_{Bi}&=5.3\ut{m/s}\\ \end{cases} $$ $$\Delta \Sigma \vec P=0,$$ $$\vec P_i=\vec P_{Af}+\vec P_{Bf},$$ $$ \begin{cases} m_Bv_i&=m_Av_{Af}+m_Bv_{Bf}\\ v_{B\larr Af}&=v_{Bf}-v_{Af} \end{cases} $$ $$v_{Af}=\frac{m_B}{m_A+m_B}(v_i-v_{B\larr Af})$$ $$\ab{a}$$ $$v_{B\larr Af}=0$$ $$ \begin{aligned} v_{Af}&=\frac{m_B}{m_A+m_B}v_i\\ &=\fr..

$$ \begin{cases} v_{Hi}&=0\\ m_H&=1840m_e \end{cases} $$ $$\Delta \Sigma \vec P=0,$$ $$v_{Bi}=0,$$ $$ \text{Elastic Collision}\Harr\vec v_{\text{in}}+ \vec v_{\text{out}}=0,$$ $$\vec v_{Ai}-\vec v_{Bi}+ \vec v_{Af}-\vec v_{Bf}=0,$$ $$ \begin{cases} \vec p_{Ai}+\vec p_{Bi}&=\vec p_{Af}+\vec p_{Bf}\\ \vec v_{Ai}+\vec v_{Af}&=\vec v_{Bi}+\vec v_{Bf}\\ \end{cases} $$ $$ \begin{cases} \vec p_{Ai}&=\v..