3. Two spheres \(A\) and \(B\), of equal radii, are moving towards each other on a smooth horizontal surface and collide directly. Sphere \(A\) has mass \(4 m \mathrm {~kg}\) and sphere \(B\) has mass \(3 m \mathrm {~kg}\). Just before the collision, \(A\) has speed \(9 \mathrm {~ms} ^ { - 1 }\) and \(B\) has speed \(3.5 \mathrm {~ms} ^ { - 1 }\). Immediately after the collision, \(A\) has speed \(1.5 \mathrm {~ms} ^ { - 1 }\) in the direction of its original motion.

1. Show that the speed of \(B\) immediately after the collision is \(6.5 \mathrm {~ms} ^ { - 1 }\).
2. Calculate the coefficient of restitution between \(A\) and \(B\).
3. Given that the magnitude of the impulse exerted by \(B\) on \(A\) is 36 Ns , find the value of \(m\).
4. Give a reason why it is not necessary to model the spheres as particles in this question.