2.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{c0993853-dd8f-4d14-aeed-b71ad60df09c-04_360_1037_260_456}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}

A uniform wooden beam $A B$, of mass 20 kg and length 4 m , rests in equilibrium in a horizontal position on two supports. One support is at $C$, where $A C = 1.6 \mathrm {~m}$, and the other support is at $D$, where $D B = 0.4 \mathrm {~m}$. A boy of mass 60 kg stands on the beam at the point $P$, where $A P = 3 \mathrm {~m}$, as shown in Figure 1. The beam remains in equilibrium in a horizontal position.

By modelling the boy as a particle and the beam as a uniform rod,
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item find, in terms of $g$, the magnitude of the force exerted on the beam by the support at $C$,
\item find, in terms of $g$, the magnitude of the force exerted on the beam by the support at $D$.

The boy now starts to walk slowly along the beam towards the end $A$.
\end{enumerate}\item Find the greatest distance he can walk from $P$ without the beam tilting.
\end{enumerate}

\hfill \mbox{\textit{Edexcel M1 2018 Q2 [10]}}