a
After \(1^{st}\) collision

\(m v_{A}=m v_{A}^{\prime}+2 m v_{B}^{\prime}\)

\(-1=\frac{v_{B}^{\prime}-v_{A}^{\prime}}{0-v_{A}} \Rightarrow v_{B}^{\prime}=6 m / s\)

After the \(2^{nd}\) collision

\(2 mv _{ B }^{\prime}=(2 m + m )_{ V _{ C }}\)

\(\Rightarrow v _{ C }=\frac{2}{3} v _{ B }^{\prime} \Rightarrow v _{ C }=4 m / s\)