5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8b85b908-bb74-4532-a1b4-3826946bd43b-3_588_291_1126_662}
\captionsetup{labelformat=empty}
\caption{Fig. 2}
\end{figure}
A firework is modelled as a uniform solid formed by joining the plane surface of a right circular cone of height \(2 r\) and base radius \(r\), to one of the plane surfaces of a cylinder of height \(h\) and base radius \(r\) as shown in Figure 2.
Using this model,
- show that the distance of the centre of mass of the firework from its plane base is
$$\frac { 3 h ^ { 2 } + 4 h r + 2 r ^ { 2 } } { 2 ( 3 h + 2 r ) }$$
The firework is to be launched from rough ground inclined at an angle \(\alpha\) to the horizontal. Given that the firework does not slip or topple and that \(h = 4 r\),
- Find, correct to the nearest degree, the maximum value of \(\alpha\).