6 Three particles \(A , B\) and \(C\) of masses \(0.3 \mathrm {~kg} , 0.4 \mathrm {~kg}\) and \(m \mathrm {~kg}\) respectively lie at rest in a straight line on a smooth horizontal plane. The distance between \(B\) and \(C\) is \(2.1 \mathrm {~m} . A\) is projected directly towards \(B\) with speed \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). After \(A\) collides with \(B\) the speed of \(A\) is reduced to \(0.6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), still moving in the same direction.

1. Show that the speed of \(B\) after the collision is \(1.05 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
   After the collision between \(A\) and \(B , B\) moves directly towards \(C\). Particle \(B\) now collides with \(C\). After this collision, the two particles coalesce and have a combined speed of \(0.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
2. Find \(m\).
3. Find the time that it takes, from the instant when \(B\) and \(C\) collide, until \(A\) collides with the combined particle.