5 A particle \(P\) is projected with speed \(u \mathrm {~ms} ^ { - 1 }\) from the top of a smooth inclined plane of length \(2 d\) metres. After its projection \(P\) moves downwards along a line of greatest slope with acceleration \(4 \mathrm {~ms} ^ { - 2 }\). At the instant 3 s after projection \(P\) has moved half way down the plane. \(P\) reaches the foot of the plane 5 s after the instant of projection.

1. Form two simultaneous equations in \(u\) and \(d\), and hence calculate the speed of projection of \(P\) and the length of the plane.
2. Find the inclination of the plane to the horizontal.
3. Given that the contact force exerted on \(P\) by the plane has magnitude 6 N , calculate the mass of \(P\).