[tex]\begin{gathered} \text{For railroad car} \\ m_r=11,600kg_{} \\ v_r=18.0\text{ m/s} \\ \text{For load} \\ m_l=3,750kg_{} \\ \text{Question} \\ v_{r+l}=_{}\text{?} \\ \\ Momentum\text{ 1= Momentum 2} \\ P1=P2 \\ P1=m_rv_r,\text{ }P2=(m_r+m_l)v_{r+l} \\ \text{Hence} \\ m_rv_r=(m_r+m_l)v_{r+l} \\ \text{Solving }v_{r+l}\text{ } \\ v_{r+l}=\frac{m_rv_r_{}}{m_r+m_l} \\ \\ v_{r+l}=\frac{(11,600kg_{})(18.0\text{ m/s})_{}}{11,600kg_{}+3,750kg_{}_{}} \\ v_{r+l}=13.6\text{ m/s} \\ \text{The new cars sp}eed\text{ is 13.6 m/s} \end{gathered}[/tex]
