3. A particle \(P\) of mass 4 kg moves from point \(A\) to point \(B\) down a line of greatest slope of a fixed rough plane. The plane is inclined at \(40 ^ { \circ }\) to the horizontal and \(A B = 12 \mathrm {~m}\). The coefficient of friction between \(P\) and the plane is 0.5

1. Find the work done against friction as \(P\) moves from \(A\) to \(B\). Given that the speed of \(P\) at \(B\) is \(24 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
2. use the work-energy principle to find the speed of \(P\) at \(A\).