4
\includegraphics[max width=\textwidth, alt={}, center]{a04e6d4e-2437-4761-87ee-43e6771fbbd9-2_332_995_1375_575} Two uniform smooth spheres \(A\) and \(B\), of equal radius, have masses 4 kg and 3 kg respectively. They are moving on a horizontal surface, and they collide. Immediately before the collision, \(A\) is moving with speed \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle \(\alpha\) to the line of centres, where \(\sin \alpha = 0.8\), and \(B\) is moving along the line of centres with speed \(12 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) (see diagram). The coefficient of restitution between the spheres is 0.5 . Find the speed and direction of motion of each sphere after the collision.
[0pt] [10]