7. A uniform sphere \(A\) of mass \(m\) is moving with speed \(u\) on a smooth horizontal table when it collides directly with another uniform sphere \(B\) of mass \(2 m\) which is at rest on the table. The spheres are of equal radius and the coefficient of restitution between them is \(e\). The direction of motion of \(A\) is unchanged by the collision.

1. Find the speeds of \(A\) and \(B\) immediately after the collision.
2. Find the range of possible values of \(e\). After being struck by \(A\), the sphere \(B\) collides directly with another sphere \(C\), of mass \(4 m\) and of the same size as \(B\). The sphere \(C\) is at rest on the table immediately before being struck by \(B\). The coefficient of restitution between \(B\) and \(C\) is also \(e\).
3. Show that, after \(B\) has struck \(C\), there will be a further collision between \(A\) and \(B\).
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