5 Two smooth spheres, $A$ and $B$, of equal radii and different masses are moving on a smooth horizontal surface when they collide.

Just before the collision, $A$ is moving with speed $5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ at an angle of $30 ^ { \circ }$ to the line of centres of the spheres, and $B$ is moving with speed $3 \mathrm {~ms} ^ { - 1 }$ perpendicular to the line of centres, as shown in the diagram below.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{719b82f7-2ab5-48db-9b2a-98284096a78a-4_314_1100_593_392}
\captionsetup{labelformat=empty}
\caption{Before collision}
\end{center}
\end{figure}

Immediately after the collision, $A$ and $B$ move with speeds $u$ and $v$ in directions which make angles of $90 ^ { \circ }$ and $40 ^ { \circ }$ respectively with the line of centres, as shown in the diagram below.\\
\includegraphics[max width=\textwidth, alt={}, center]{719b82f7-2ab5-48db-9b2a-98284096a78a-4_392_1102_1155_392}
\begin{enumerate}[label=(\alph*)]
\item Show that $v = 4.67 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, correct to three significant figures.
\item Find the coefficient of restitution between the spheres.
\item Given that the mass of $A$ is 0.5 kg , show that the magnitude of the impulse exerted on $A$ during the collision is 2.17 Ns , correct to three significant figures.
\item Find the mass of $B$.
\end{enumerate}

\hfill \mbox{\textit{AQA M3 2009 Q5 [12]}}