4 Ken is trying to cross a river of width 4 m . He has a uniform plank, $A B$, of length 8 m and mass 17 kg . The ground on both edges of the river bank is horizontal. The plank rests at two points, $C$ and $D$, on fixed supports which are on opposite sides of the river. The plank is at right angles to both river banks and is horizontal. The distance $A C$ is 1 m , and the point $C$ is at a horizontal distance of 0.6 m from the river bank. Ken, who has mass 65 kg , stands on the plank directly above the middle of the river, as shown in the diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{31ba38f7-38a8-4e4e-96a3-19e819fabfb0-3_468_1086_1710_479}
\begin{enumerate}[label=(\alph*)]
\item Draw a diagram to show the forces acting on the plank.
\item Given that the reaction on the plank at the point $D$ is $44 g \mathrm {~N}$, find the horizontal distance of the point $D$ from the nearest river bank.
\item State how you have used the fact that the plank is uniform in your solution.
\end{enumerate}

\hfill \mbox{\textit{AQA M2 2011 Q4 [7]}}