The initial momentum of the system is,
[tex]p_i=m_1u_1+m_2u_2[/tex]The final momentum of the system is,
[tex]p_f=(m_1+m_2)v[/tex]According to conservation of momentum,
[tex]p_i=p_f[/tex]Plug in the known expressions,
[tex]\begin{gathered} m_1u_1+m_2u_2=(m_1+m_{2_{}})v \\ v=\frac{m_1u_1+m_2u_2}{m_1+m_2} \end{gathered}[/tex]Substitute the known values,
[tex]\begin{gathered} v=\frac{(1415\text{ kg)(22.9 m/s)+(819 kg)(11 m/s)}}{(1415\text{ kg+819 kg)}} \\ =\frac{32403.5\text{ kgm/s+}9009\text{ kgm/s}}{2234\text{ kg}} \\ =\frac{41412.5\text{ kgm/s}}{2234\text{ kg}} \\ \approx18.5\text{ m/s} \end{gathered}[/tex]Therefore, the total velocity after the collision is 18.5 m/s
