3. A beam \(A B\) has length 15 m and mass 25 kg . The beam is smoothly supported at the point \(P\), where \(A P = 8 \mathrm {~m}\). A man of mass 100 kg stands on the beam at a distance of 2 m from \(A\) and another man stands on the beam at a distance of 1 m from \(B\). The beam is modelled as a non-uniform rod and the men are modelled as particles. The beam is in equilibrium in a horizontal position with the reaction on the beam at \(P\) having magnitude 2009 N. Find the distance of the centre of mass of the beam from \(A\).