3rd ball says: Ouch It Hurts!

Three balls are kept on a straight line on a smooth surface. The first ball of mass m1{ m }_{ 1 } is projected with velocity Vo{ V }_{ o } towards the middle ball of mass m2{ m }_{ 2 }, which then collides with the third ball of mass m3{ m }_{ 3 }.

If we want m3{ m }_{ 3 } to move with the maximum possible velocity, then what should be the mass of m2{ m }_{ 2 } in kg? All collisions are elastic.

Details\textit{Details}

Use the following data if needed :

m1=4kgm3=9kgVo=16m/s\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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