1. Two particles, \(A\) and \(B\), are moving in opposite directions along the same straight line on a smooth horizontal surface when they collide directly.

Particle \(A\) has mass \(5 m\) and particle \(B\) has mass \(3 m\).
The coefficient of restitution between \(A\) and \(B\) is \(e\), where \(e > 0\)
Immediately after the collision the speed of \(A\) is \(v\) and the speed of \(B\) is \(2 v\).
Given that \(A\) and \(B\) are moving in the same direction after the collision,

1. find the set of possible values of \(e\). Given also that the kinetic energy of \(A\) immediately after the collision is \(16 \%\) of the kinetic energy of \(A\) immediately before the collision,
2. find
   1. the value of \(e\),
   2. the magnitude of the impulse received by \(A\) in the collision, giving your answer in terms of \(m\) and \(v\).