6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{96e004d9-c6b6-474b-9b67-06e1771c609e-12_554_780_246_223}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{96e004d9-c6b6-474b-9b67-06e1771c609e-12_554_706_246_1133}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
Figure 2 shows the entrance to a road tunnel. The maximum height of the tunnel is measured as 5 metres and the width of the base of the tunnel is measured as 6 metres.
Figure 3 shows a quadratic curve \(B C A\) used to model this entrance.
The points \(A , O , B\) and \(C\) are assumed to lie in the same vertical plane and the ground \(A O B\) is assumed to be horizontal.
- Find an equation for curve \(B C A\).
A coach has height 4.1 m and width 2.4 m .
- Determine whether or not it is possible for the coach to enter the tunnel.
- Suggest a reason why this model may not be suitable to determine whether or not the coach can pass through the tunnel.