9-25 할리데이 11판 솔루션 일반물리학

$$ \put \begin{cases} S:\text{Ship}\\ J:\text{Jupiter}\\ \end{cases} $$ $$ \begin{cases} m_S&=m\\ m_J&=M\\ v_{Si}&=10.5\ut{km/s}\\ v_{Ji}&=13.0\ut{km/s}\\ m_J&\gg m_S\\ \end{cases} $$ $$ \begin{cases} \Delta \Sigma \vec P=0,\\ \text{Elastic Collision}\Harr\vec v_{\text{in}}+ \vec v_{\text{out}}=0, \end{cases} $$ $$ \begin{cases} m_Sv_{Si}+m_Jv_{Ji}=m_Sv_{Sf}+m_Jv_{Jf}\\ v_{Si}-v_{Ji}+v_{Sf}-v_{Jf}=0 \end{cases} $$ $$ \begin{aligned} v_{Sf}&=\frac{2 m_J v_{Ji}-(m_J-m_S)v_{Si}}{m_J+m_S}\\ &=2\frac{ m_J }{m_J+m_S}v_{Ji}-\frac{m_J-m_S}{m_J+m_S}v_{Si}\\ &\approx 2\frac{ m_J }{m_J+0}v_{Ji}-\frac{m_J-0}{m_J+0}v_{Si}~~~(\because m_J\gg m_S)\\ &\approx 2v_{Ji}-v_{Si}\\ &\approx 15.5\ut{km/s} \end{aligned} $$