9.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{2ce10759-9ce6-47a1-b55d-d22082f88f55-22_595_1058_248_466}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
The graph in Figure 3 shows the path of a small ball.
The ball travels in a vertical plane above horizontal ground.
The ball is thrown from the point represented by \(A\) and caught at the point represented by \(B\).
The height, \(H\) metres, of the ball above the ground has been plotted against the horizontal distance, \(x\) metres, measured from the point where the ball was thrown.
With respect to a fixed origin \(O\), the point \(A\) has coordinates \(( 0,2 )\) and the point \(B\) has coordinates (20, 0.8), as shown in Figure 3.
The ball reaches its maximum height when \(x = 9\)
A quadratic function, linking \(H\) with \(x\), is used to model the path of the ball.
- Find \(H\) in terms of \(x\).
- Give one limitation of the model.
Chandra is standing directly under the path of the ball at a point 16 m horizontally from \(O\).
Chandra can catch the ball if the ball is less than 2.5 m above the ground.
- Use the model to determine if Chandra can catch the ball.