A small ball \(A\) of mass \(3 m\) is moving with speed \(u\) in a straight line on a smooth horizontal table. The ball collides directly with another small ball \(B\) of mass \(m\) moving with speed \(u\) towards \(A\) along the same straight line. The coefficient of restitution between \(A\) and \(B\) is \(\frac { 1 } { 2 }\). The balls have the same radius and can be modelled as particles.
Find
the speed of \(A\) immediately after the collision,
the speed of \(B\) immediately after the collision.
After the collision \(B\) hits a smooth vertical wall which is perpendicular to the direction of motion of \(B\). The coefficient of restitution between \(B\) and the wall is \(\frac { 2 } { 5 }\).
Find the speed of \(B\) immediately after hitting the wall.
The first collision between \(A\) and \(B\) occurred at a distance 4a from the wall. The balls collide again \(T\) seconds after the first collision.