From Mechanics

Using

\displaystyle {{m}_{A}}{{\mathbf{v}}_{A}}+{{m}_{B}}{{\mathbf{v}}_{B}}={{m}_{A}}{{\mathbf{u}}_{A}}+{{m}_{B}}{{\mathbf{u}}_{B}}

and

\displaystyle {{\mathbf{u}}_{A}}={{\mathbf{u}}_{B}}

Assume the particles have mass \displaystyle m

\displaystyle \begin{align} & m(5\mathbf{i})+m(8\mathbf{j})=2m\mathbf{v} \\ & \mathbf{v}=2\textrm{.}5\mathbf{i}+4\mathbf{j} \\ & v=\sqrt{{{2\textrm{.}5}^{2}}+{{4}^{2}}}=4\textrm{.}72\text{ m}{{\text{s}}^{\text{-1}}} \\ \end{align}