8 A uniform ladder \(A B\), of weight 150 N and length 4 m , rests in equilibrium with the end \(A\) in contact with rough horizontal ground and the end \(B\) resting against a smooth vertical wall. The ladder is inclined at an angle \(\theta\) to the horizontal, where \(\tan \theta = 3\). A man of weight 750 N is standing on the ladder at a distance \(x \mathrm {~m}\) from \(A\).

1. Show that the magnitude of the frictional force exerted by the ground on the ladder is \(\frac { 25 } { 2 } ( 2 + 5 x ) \mathrm { N }\). The coefficient of friction between the ladder and the ground is \(\frac { 1 } { 4 }\).
2. Find the greatest value of \(x\) for which equilibrium is possible.