3. A particle \(P\) of mass 4 kg is projected with speed \(6 \mathrm {~ms} ^ { - 1 }\) up a line of greatest slope of a fixed rough inclined plane. The plane is inclined at angle \(\alpha\) to the horizontal, where \(\sin \alpha = \frac { 1 } { 7 }\). The particle is projected from the point \(A\) on the plane and comes to instantaneous rest at the point \(B\) on the plane, where \(A B = 10 \mathrm {~m}\).

1. Show that the work done against friction as \(P\) moves from \(A\) to \(B\) is 16 joules. After coming to instantaneous rest at \(B\), the particle slides back down the plane.
2. Use the work-energy principle to find the speed of \(P\) at the instant it returns to \(A\).