6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4c8ebad3-0ebb-4dfe-8036-54b651deb9cf-10_506_1361_205_299}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
A cricket ball is hit from a point \(A\) with velocity of \(( p \mathbf { i } + q \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\), at an angle \(\alpha\) above the horizontal. The unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are respectively horizontal and vertically upwards. The point \(A\) is 0.9 m vertically above the point \(O\), which is on horizontal ground.
The ball takes 3 seconds to travel from \(A\) to \(B\), where \(B\) is on the ground and \(O B = 57.6 \mathrm {~m}\), as shown in Figure 3. By modelling the motion of the cricket ball as that of a particle moving freely under gravity,
- find the value of \(p\),
- show that \(q = 14.4\),
- find the initial speed of the cricket ball,
- find the exact value of \(\tan \alpha\).
- Find the length of time for which the cricket ball is at least 4 m above the ground.
- State an additional physical factor which may be taken into account in a refinement of the above model to make it more realistic.