\(m(0)=\frac{2 m}{5}(-v \hat{i})+\frac{2 m}{5}(-v \hat{j})+\frac{m}{5} \vec{v}^{\prime}\)

\(\Rightarrow \vec{v}^{\prime}=2 v \hat{i}+2 v \hat{j}\)

\(\Rightarrow v^{\prime}=\sqrt{(2 v)^{2}+(2 v)^{2}}\)

\(=2 \sqrt{2} v\)