6. Figure 3 A uniform pole \(A B\), of weight 50 N and length 6 m , has a particle of weight \(W\) newtons attached at its end \(B\). The pole has its end \(A\) freely hinged to a vertical wall.
A light rod holds the particle and pole in equilibrium with the pole at \(60 ^ { \circ }\) to the wall. One end of the light rod is attached to the pole at \(C\), where \(A C = 4 \mathrm {~m}\).
The other end of the light rod is attached to the wall at the point \(D\).
The point \(D\) is vertically below \(A\) with \(A D = 4 \mathrm {~m}\), as shown in Figure 3.
The pole and the light rod lie in a vertical plane which is perpendicular to the wall.
The pole is modelled as a rod.
Given that the thrust in the light rod is \(60 \sqrt { 3 } \mathrm {~N}\),

1. show that \(W = 15\)
2. find the magnitude of the resultant force acting on the pole at \(A\).