5 Two particles \(A\) and \(B\) are on a smooth horizontal floor with \(B\) between \(A\) and a vertical wall. The masses of \(A\) and \(B\) are 4 kg and 11 kg respectively. Initially, \(B\) is at rest and \(A\) is moving towards \(B\) with a speed of \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\) (see diagram). \(A\) collides directly with \(B\). The coefficient of restitution between \(A\) and \(B\) is \(e\).
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1. Show that immediately after the collision the speed of \(B\) is \(\frac { 4 } { 15 } u ( 1 + e )\). After the collision between \(A\) and \(B\) the direction of motion of \(A\) is reversed. \(B\) subsequently collides directly with the vertical wall. The coefficient of restitution between \(B\) and the wall is \(\frac { 1 } { 2 } e\).
2. Given that there is a second collision between \(A\) and \(B\), find the range of possible values of \(e\).