1. A rough plane is inclined to the horizontal at an angle \(\theta\), where \(\tan \theta = \frac { 3 } { 4 }\)

A particle \(P\) of mass \(m\) is at rest at a point on the plane. The particle is projected up the plane with speed \(\sqrt { 2 a g }\)
The particle moves up a line of greatest slope of the plane and comes to instantaneous rest after moving a distance \(d\). The coefficient of friction between \(P\) and the plane is \(\frac { 1 } { 7 }\)

1. Show that the magnitude of the frictional force acting on \(P\) as it moves up the plane is \(\frac { 4 m g } { 35 }\) Air resistance is assumed to be negligible.
   Using the work-energy principle,
2. find \(d\) in terms of \(a\).