A particle \(P\) is projected with speed \(u\,\text{m s}^{-1}\) at an angle \(\theta\) above the horizontal from a point \(O\), and moves freely under gravity.

After \(5\) seconds the speed of \(P\) is \(\dfrac34u\).

(a) Show that

(b) It is given that the velocity of \(P\) after \(5\) seconds is perpendicular to the initial velocity. Find, in either order, \(u\) and \(\sin\theta\).