A small block of mass 3 kg is initially at rest at the bottom O of a rough plane inclined at an angle \(\alpha\) to the horizontal, where \(\sin \alpha = 0.6\) and \(\cos \alpha = 0.8\). A force of magnitude 35 N acts on the block at an angle \(\beta\) above the plane, where \(\sin \beta = 0.28\) and \(\cos \beta = 0.96\). The block starts to move up a line of greatest slope of the plane and passes through a point A with speed 4 m s\(^{-1}\). The distance \(OA\) is 12.5 m (see diagram).

(i) For the motion of the block from \(O\) to \(A\), find the work done against the frictional force acting on the block.

(ii) Find the coefficient of friction between the block and the plane.

At the instant that the block passes through \(A\) the force of magnitude 35 N ceases to act.

(iii) Find the distance the block travels up the plane after passing through \(A\).