Two small smooth balls \(A\) and \(B\) have mass 0.6 kg and 0.9 kg respectively. They are moving in a straight line towards each other in opposite directions on a smooth horizontal floor and collide directly. Immediately before the collision the speed of \(A\) is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and the speed of \(B\) is \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The speed of \(A\) is \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) immediately after the collision and \(B\) is brought to rest by the collision.
Find
the value of \(v\),
the magnitude of the impulse exerted on \(A\) by \(B\) in the collision.