4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{86a37170-046f-46e5-9c8c-06d5f98ca4fe-12_387_929_246_568}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
Two smooth uniform spheres, \(A\) and \(B\), have equal radii. The mass of \(A\) is \(3 m\) and the mass of \(B\) is \(4 m\). The spheres are moving on a smooth horizontal plane when they collide obliquely. Immediately before they collide, \(A\) is moving with speed \(3 u\) at \(30 ^ { \circ }\) to the line of centres of the spheres and \(B\) is moving with speed \(2 u\) at \(30 ^ { \circ }\) to the line of centres of the spheres. The direction of motion of \(B\) is turned through an angle of \(90 ^ { \circ }\) by the collision, as shown in Figure 3.
- Find the size of the angle through which the direction of motion of \(A\) is turned as a result of the collision.
- Find, in terms of \(m\) and \(u\), the magnitude of the impulse received by \(B\) in the collision.