3 A uniform ladder $P Q$, of length 8 metres and mass 28 kg , rests in equilibrium with its foot, $P$, on a rough horizontal floor and its top, $Q$, leaning against a smooth vertical wall. The vertical plane containing the ladder is perpendicular to the wall and the angle between the ladder and the floor is $69 ^ { \circ }$.

A man, of mass 72 kg , is standing at the point $C$ on the ladder so that the distance $P C$ is 6 metres. The man may be modelled as a particle at $C$.\\
\includegraphics[max width=\textwidth, alt={}, center]{06c3e260-8167-4616-97d4-0f360a376a0f-3_679_679_685_678}
\begin{enumerate}[label=(\alph*)]
\item Draw a diagram to show the forces acting on the ladder.
\item With the man standing at the point $C$, the ladder is on the point of slipping.
\begin{enumerate}[label=(\roman*)]
\item Show that the magnitude of the reaction between the ladder and the vertical wall is 256 N , correct to three significant figures.
\item Find the coefficient of friction between the ladder and the horizontal floor.
\end{enumerate}\end{enumerate}

\hfill \mbox{\textit{AQA M2 2012 Q3 [10]}}