6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f5449ec3-ead0-464f-9d03-f225cd21bca6-4_412_770_198_507}
\captionsetup{labelformat=empty}
\caption{Fig. 2}
\end{figure}
A football player strikes a ball giving it an initial speed of \(14 \mathrm {~ms} ^ { - 1 }\) at an angle \(\alpha\) to the horizontal as shown in Figure 2. At the instant he strikes the ball it is 0.6 m vertically above the point \(P\) on the ground. The trajectory of the ball is in a vertical plane containing \(P\) and \(M\), the middle of the goal-line. The distance between \(P\) and \(M\) is 12 m and the ground is horizontal.
Given that the ball passes over the point \(M\) without bouncing,
- find, to the nearest degree, the minimum value of \(\alpha\).
Given that the crossbar of the goal is 2.4 m above \(M\) and that \(\tan \alpha = \frac { 4 } { 3 }\),
- show that the ball passes 4.2 m vertically above the crossbar.