9-59 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} m_2&=1.0\ut{kg}\\ v_{2i}&=0\\ k&=490\ut{N/m}\\ m_1&=2.0\ut{kg}\\ M&=m_1+m_2=3\ut{kg}\\ v_{1i}&=4.0\ut{m/s}\\ \end{cases} $$ $$\Delta \Sigma \vec p=0,$$ $$ \begin{aligned} m_1v_{1i}&=Mv_f,\\ v_f&=\frac{m_1}{M}v_{1i} \end{aligned} $$ $$\Sigma \Delta E=0,$$ $$\frac{1}{2}M{v_f}^2=\frac{1}{2}kx^2$$ $$ \begin{aligned} x&=v_f\sqrt\frac{M}{k}\\ &=\frac{m_1v_{1i}}{\sqrt{Mk}}\\ &=\frac{4}{7}\sqrt{\frac{2}{15}}\ut{m}\\ &\approx 0.2086562123829204\ut{m}\\ &\approx 0.21\ut{m}\\ &\approx 21\ut{cm}\\ \end{aligned} $$