1. \section*{Figure 1} Figure 1 A particle of mass \(m\) is held at rest at a point \(A\) on a rough plane.
The plane is inclined at an angle \(\alpha\) to the horizontal, where \(\tan \alpha = \frac { 5 } { 12 }\)
The coefficient of friction between the particle and the plane is \(\frac { 1 } { 5 }\)
The points \(A\) and \(B\) lie on a line of greatest slope of the plane, with \(B\) above \(A\), and \(A B = d\), as shown in Figure 1. The particle is pushed up the line of greatest slope from \(A\) to \(B\).

1. Show that the work done against friction as the particle moves from \(A\) to \(B\) is \(\frac { 12 } { 65 } m g d\) The particle is then held at rest at \(B\) and released.
2. Use the work-energy principle to find, in terms of \(g\) and \(d\), the speed of the particle at the instant it reaches \(A\).