3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4878b6c2-0c62-4398-8a8f-913139bc8a14-04_245_860_260_543}
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\caption{Figure 1}
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A uniform beam \(A B\) has mass 20 kg and length 6 m . The beam rests in equilibrium in a horizontal position on two smooth supports. One support is at \(C\), where \(A C = 1 \mathrm {~m}\), and the other is at the end \(B\), as shown in Figure 1. The beam is modelled as a rod.
- Find the magnitudes of the reactions on the beam at \(B\) and at \(C\).
A boy of mass 30 kg stands on the beam at the point \(D\). The beam remains in equilibrium. The magnitudes of the reactions on the beam at \(B\) and at \(C\) are now equal. The boy is modelled as a particle.
- Find the distance \(A D\).