3rd ball says: Ouch It Hurts!

Three balls are kept on a straight line on a smooth surface. The first ball of mass \({ m }_{ 1 }\) is projected with velocity \({ V }_{ o }\) towards the middle ball of mass \({ m }_{ 2 }\), which then collides with the third ball of mass \({ m }_{ 3 }\).

If we want \({ m }_{ 3 }\) to move with the maximum possible velocity, then what should be the mass of \({ m }_{ 2 }\) in kg? All collisions are elastic.

\(\textit{Details}\)

Use the following data if needed :

\(\bullet \quad { m }_{ 1 }\quad =\quad 4\quad kg \\ \bullet \quad { m }_{ 3 }\quad =\quad 9\quad kg \\ \bullet \quad { V }_{ o }\quad =\quad 16\quad m/s\)

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