6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{725966d1-d29d-4c9d-b850-c67d55cdd6e8-07_629_835_306_497}
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\caption{Figure 1}
\end{figure}
A stone is thrown over level ground from the top of a tower, \(X\).
The height, \(h\), in meters, of the stone above the ground level after \(t\) seconds is modelled by the function.
$$\mathrm { h } ( t ) = 7 + 21 t - 4.9 t ^ { 2 } , t \geq 0$$
A sketch of \(h\) against \(t\) is shown in Figure 1.
Using the model,
a. give a physical interpretation of the meaning of the constant term 7 in the model.
b. find the time taken after the stone is thrown for it to reach ground level.
c. Rearrange \(\mathrm { h } ( t )\) into the form \(A - B ( t - C ) ^ { 2 }\), where \(A , B\) and \(C\) are constants to be found.
d. Using your answer to part cor otherwise, find the maximum height of the stone above the ground, and the time after which this maximum height is reached.