- \hspace{0pt} [In this question, \(\mathbf { i }\) and \(\mathbf { j }\) are perpendicular unit vectors in a horizontal plane.]
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{361d263e-0ee1-47e9-8fc2-0f127f1c2d7e-12_588_633_301_724}
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\caption{Figure 1}
\end{figure}
Figure 1 represents the plan view of part of a smooth horizontal floor, where \(A B\) represents a fixed smooth vertical wall.
A small ball of mass 0.5 kg is moving on the floor when it strikes the wall.
Immediately before the impact the velocity of the ball is \(( 7 \mathbf { i } + 2 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\).
Immediately after the impact the velocity of the ball is \(( \mathbf { i } + 6 \mathbf { j } ) \mathrm { ms } ^ { - 1 }\).
The coefficient of restitution between the ball and the wall is \(e\).
- Show that \(A B\) is parallel to \(( 2 \mathbf { i } + 3 \mathbf { j } )\).
- Find the value of \(e\).