5 A particle \(P\) is projected from a point \(O\) on a horizontal plane and moves freely under gravity. Its initial speed is \(u \mathrm {~ms} ^ { - 1 }\) and its angle of projection is \(\sin ^ { - 1 } \left( \frac { 4 } { 5 } \right)\) above the horizontal. At time 8 s after projection, \(P\) is at the point \(A\). At time 32 s after projection, \(P\) is at the point \(B\). The direction of motion of \(P\) at \(B\) is perpendicular to its direction of motion at \(A\). Find the value of \(u\).