솔루션피아

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

$$ \begin{cases} m_A&=0.270\ut{kg}\\ \vec v_{\text{in}}&=-12.0\j\ut{m/s}\\ \vec v_{\text{out}}&=+3.00\j\ut{m/s}\\ \vec v_B&=0 \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} \Delta \vec P_A&=\Delta (m_A\vec v_A)\\ &=m_A\Delta \vec v_A\\ &=m_A (\vec v_{Af}-\vec v_{Ai})\\ &=m_A (\vec v_{\text{out}}-\vec v_{\text{in}})\\ &=\frac{81}{20}\j\ut{kg\cdot m/s}\\ &=4.05\j\ut{kg\cdot m/s}\\ \end{aligned} $$ $..

$$ \begin{cases} m_A&=75\ut{kg}\\ m_B&=50\ut{kg}\\ v_i&=2.3\ut{m/s}\\ v_{Af}&=0 \end{cases} $$ $$\Delta \Sigma \vec P=0,$$ $$ \begin{aligned} \vec P_i&=\vec P_{Af}+\vec P_{Bf}\\ (m_A+m_B)v_i&=m_Av_{Af}+m_Bv_{Bf}\\ &=m_Bv_{Bf}\\ \end{aligned} $$ $$ v_{Bf}=\frac{m_A+m_B}{m_B}v_i $$ $$ \begin{aligned} \Delta v_B&=v_{Bf}-v_{Bi}\\ &=\frac{m_A+m_B}{m_B}v_i-v_{i}\\ &=\frac{m_A}{m_B}v_i\\ &=+\frac{69}{2..

$$ \put \begin{cases} A:m_1\\ B:m_2\\ C:m_3\\ \end{cases} $$ $$ \put \begin{cases} 0:\text{Start}\\ 1:\text{After A,B Crash}\\ 2:\text{After B,C Crash}\\ \end{cases} $$ $$ \begin{cases} m_A&=4m\\ m_B&=0.500m_A=2m\\ m_C&=0.500m_B=m \end{cases} $$ $$ \begin{cases} v_{A0}&=2.00\ut{m/s}\\ v_{B0}&=0\\ v_{C0}&=0\\ \end{cases} $$ $$\Delta \Sigma \vec P=0,$$ $$ \text{Elastic Collision}\Harr\vec v_{\text..