6 Two smooth circular discs \(A\) and \(B\) are moving on a horizontal plane. The masses of \(A\) and \(B\) are 3 kg and 4 kg respectively. At the instant before they collide
- the velocity of \(A\) is \(2 \mathrm {~ms} ^ { - 1 }\) at an angle of \(60 ^ { \circ }\) to the line joining their centres,
- the velocity of \(B\) is \(5 \mathrm {~ms} ^ { - 1 }\) towards \(A\) along the line joining their centres (see Fig. 6).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{831ba5da-df19-43bb-b163-02bbddb4e2b8-5_490_1047_470_244}
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\caption{Fig. 6}
\end{figure}
Given that the velocity of \(A\) after the collision is perpendicular to the velocity of \(A\) before the collision, find
- the coefficient of restitution between \(A\) and \(B\),
- the total loss of kinetic energy as a result of the collision.