9-61 할리데이 11판 솔루션 일반물리학

$$ \put \begin{cases} s:\text{ship}\\ g:\text{gas}\\ \end{cases} $$ $$\put \dot y=\dyt{y},$$ $$ \begin{cases} v_i&=6.0\times10^3\ut{m/s}\\ v_{g\larr s}&=-3.0\times10^3\ut{m/s}\\ m_s&=2.5\times10^4\ut{kg}\\ a_s&=2.0\ut{m/s^2}\\ M&=m_s+m_g\\ \end{cases} $$ $$\Delta \Sigma \vec p=0,$$ $$ \begin{cases} Mv_i&=m_gv_{g}+m_sv_s\\ v_{g\larr s}&=v_g-v_s\\ \Delta v_s&=v_s-v_i \end{cases} $$ $$ \begin{aligned} -m_gv_{g\larr s}&=M\Delta v_s\\ \dt(-m_gv_{g\larr s})&=\dt(M\Delta v_s)\\ \dyt{m_g}(-v_{g\larr s})&=M\dyt{\Delta v_s}\\ \dot{m_g}(-v_{g\larr s})&=Ma_s \end{aligned} $$ $$\ab{a}$$ $$ \begin{aligned} F_{\text{Thrust}}&=Ma\\ &=5.0\times10^5\ut{N}\\ &=0.50\ut{MN}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} \dot{m_g}&=\frac{Ma_s}{-v_{g\larr s}}\\ &=\frac{50}{3}\ut{kg/s}\\ &\approx 16.666666666666668\ut{kg/s}\\ &\approx 17\ut{kg/s}\\ \end{aligned} $$