8 A girl stands at the edge of a quay and sees a tin can floating in the water. The water level is 5 metres below the top of the quay and the can is at a horizontal distance of 10 metres from the quay, as shown in the diagram.\\
\begin{tikzpicture}[>=latex]
 
  % Quay (filled rectangle)
  \draw[thick, fill=gray!25] (-5,0) rectangle (0,5);
  \node at (-2.5,2.5) {Quay};
 
  % Ground line
  \draw[thick] (0,0) -- (11.5,0);
 
  % Small box on the ground at 10 m
  \draw[thick, fill=white] (9.8,-0.25) rectangle (10.2,0.25);
 
  % Person (circle) over the edge of the quay
  \fill (0.5,5.7) circle (0.2);
 
  % 5 metres label (height of quay)
  \draw[<->] (1.5,0) -- node[right] {5 metres} (1.5,5);
 
  % 10 metres label
  \draw[<->] (0,-0.8) -- node[below] {10 metres} (10,-0.8);
 
\end{tikzpicture}

The girl decides to throw a stone at the can. She throws the stone from a height of 1 metre above the top of the quay. The initial velocity of the stone is $8 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ at an angle $\alpha$ below the horizontal, so that the initial velocity of the stone is directed at the can, as shown in the diagram.\\
\begin{tikzpicture}[>=latex]
 
  % Quay (filled rectangle)
  \draw[thick, fill=gray!25] (-5,0) rectangle (0,5);
  \node at (-2.5,2.5) {Quay};
 
  % Ground line
  \draw[thick] (0,0) -- (11.5,0);
 
  % Small box on the ground at 10 m
  \draw[thick, fill=white] (9.8,-0.25) rectangle (10.2,0.25);
 
  % Person (circle) over the edge of the quay
  \fill (0.5,5.7) circle (0.2);
 
  % 5 metres label (height of quay)
  \draw[<->] (1.5,0) -- node[right] {5 metres} (1.5,5);
 
  % 10 metres label
  \draw[<->] (0,-0.8) -- node[below] {10 metres} (10,-0.8);
 
  % 1 metre label
  \draw[<->] (-0.8,5) -- node[left] {1 metre} (-0.8,6);
 
  % Dashed horizontal line at release height
  \draw[dashed] (-1.2,6) -- (3,6);
 
  % Angle arc for alpha
  \draw (2,6) arc[start angle=0, end angle=-32, radius=1.5];
  \node at (2.5,5.55) {$\alpha$};
 
  % Velocity arrow
  \draw[thick,->] (0.5,6) -- +(-32:2.5) node[right] {8\,m\,s$^{-1}$};
 
  % Dashed trajectory curve
  \draw[dashed, thick] (0.5, 6) -- (10, 0);
 
\end{tikzpicture}

Assume that the stone is a particle and that it experiences no air resistance as it moves.
\begin{enumerate}[label=(\alph*)]
\item Find $\alpha$.
\item Find the time that it takes for the stone to reach the level of the water.
\item Find the distance between the stone and the can when the stone hits the water.
\end{enumerate}

\hfill \mbox{\textit{AQA M1 2012 Q8 [12]}}