7. A particle \(P\) has mass 4 kg . It is projected from a point \(A\) up a line of greatest slope of a rough plane inclined at an angle \(\alpha\) to the horizontal, where \(\tan \alpha = \frac { 3 } { 4 }\). The coefficient of friction between \(P\) and the plane is \(\frac { 2 } { 7 }\). The particle comes to rest instantaneously at the point \(B\) on the plane, where \(A B = 2.5 \mathrm {~m}\). It then moves back down the plane to \(A\).

1. Find the work done by friction as \(P\) moves from \(A\) to \(B\).
2. Using the work-energy principle, find the speed with which \(P\) is projected from \(A\).
3. Find the speed of \(P\) when it returns to \(A\).