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\includegraphics[max width=\textwidth, alt={}, center]{43ed8ec7-67f1-418a-8d4e-ee96448647fd-2_544_816_781_603} Two uniform smooth spheres \(A\) and \(B\), of equal radius, have masses \(2 m \mathrm {~kg}\) and \(m \mathrm {~kg}\) respectively. They are moving in opposite directions on a horizontal surface and they collide. Immediately before the collision, each sphere has speed \(u \mathrm {~ms} ^ { - 1 }\) in a direction making an angle \(\alpha\) with the line of centres (see diagram). The coefficient of restitution between \(A\) and \(B\) is 0.5 .

1. Show that the speed of \(B\) is unchanged as a result of the collision.
2. Find the direction of motion of each of the spheres after the collision.