4.
\section*{Figure 1}
\includegraphics[max width=\textwidth, alt={}]{0d3d35b1-e3c5-47ac-b05e-78cdf1eb3083-3_714_565_262_749}
A uniform ladder, of mass \(m\) and length \(2 a\), has one end on rough horizontal ground. The other end rests against a smooth vertical wall. A man of mass \(3 m\) stands at the top of the ladder and the ladder is in equilibrium. The coefficient of friction between the ladder and the ground is \(\frac { 1 } { 4 }\), and the ladder makes an angle \(\alpha\) with the vertical, as shown in Fig. 1. The ladder is in a vertical plane perpendicular to the wall.
Show that \(\tan \alpha \leq \frac { 2 } { 7 }\).