4.
\begin{figure}[h]
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\caption{Figure 4}
\includegraphics[alt={},max width=\textwidth]{51510155-a8cc-4e70-8ffa-44ed35618261-4_284_1077_294_429}
\end{figure}
In a game at a fair, a small target \(C\) moves horizontally with simple harmonic motion between the points \(A\) and \(B\), where \(A B = 4 L\). The target moves inside a box and takes 3 s to travel from \(A\) to \(B\). A player has to shoot at \(C\), but \(C\) is only visible to the player when it passes a window \(P Q\), where \(P Q = b\). The window is initially placed with \(Q\) at the point as shown in Figure 4. The target \(C\) takes 0.75 s to pass from \(Q\) to \(P\).
- Show that \(b = ( 2 - \sqrt { 2 } ) L\).
- Find the speed of \(C\) as it passes \(P\).
\begin{figure}[h]
\captionsetup{labelformat=empty}
\caption{Figure 5}
\includegraphics[alt={},max width=\textwidth]{51510155-a8cc-4e70-8ffa-44ed35618261-4_286_1082_1327_424}
\end{figure}
For advanced players, the window \(P Q\) is moved to the centre of \(A B\) so that \(A P = Q B\), as shown in Figure 5. - Find the time, in seconds to 2 decimal places, taken for \(C\) to pass from \(Q\) to \(P\) in this new position.