Recall that the relative velocity is independent of the reference frame, \[\overrightarrow{\mathbf{v}}_{1, i}-\overrightarrow{\mathbf{v}}_{2, i}=\overrightarrow{\mathbf{v}}_{1, i}^{\prime}-\overrighta...Recall that the relative velocity is independent of the reference frame, \[\overrightarrow{\mathbf{v}}_{1, i}-\overrightarrow{\mathbf{v}}_{2, i}=\overrightarrow{\mathbf{v}}_{1, i}^{\prime}-\overrightarrow{\mathbf{v}}_{2, i}^{\prime} \nonumber \] In the laboratory reference frame \(\overrightarrow{\mathbf{v}}_{2, i}=\overrightarrow{\mathbf{0}}\), hence the initial relative velocity is \(\overrightarrow{\mathbf{v}}_{1,2, i}^{\prime}=\overrightarrow{\mathbf{v}}_{1,2, i}=\overrightarrow{\mathbf{v}}…
