Two uniform spheres, \(A\) and \(B\), have the same radius. The mass of \(A\) is \(0.4 \text{kg}\) and the mass of \(B\) is \(0.2 \text{kg}\). The spheres \(A\) and \(B\) are travelling in the same direction in a straight line on a smooth horizontal surface, \(A\) with speed \(5 \text{ms}^{−1}\) , and \(B\) with speed \(V \text{ms}^{−1}\) , where \(V < 5\). A collides directly with \(B\) and the impulse between them has magnitude \(0.9 \text{Ns}\). Immediately after the collision, the speed of \(B\) is \(6 \text{ms}^{−1}\) .

\((\text{i})\) Calculate \(V\).

\(B\) subsequently collides directly with a stationary sphere \(C\) of mass \(0.1 \text{kg}\) and the same radius as \(A\) and \(B\). The coefficient of restitution between \(B\) and \(C\) is \(0.6\).

\((\text{ii})\) Determine whether there will be a further collision between \(A\) and \(B\).

**Input \(V\) if a further collision takes place, otherwise input \(2V\), to three significant figures.**

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