A particle \(P\) is projected from a point \(O\) on horizontal ground with speed \(u\) at an angle \(\theta\) above the horizontal, where \(\tan\theta=\dfrac13\). The particle moves freely under gravity and passes through the point with coordinates \(\left(3a,\dfrac45a\right)\), relative to horizontal and vertical axes through \(O\).

(a) Use the equation of the trajectory to show that \(u^2=25ag\).

At the instant when \(P\) is moving horizontally, a particle \(Q\) is projected from \(O\) with speed \(V\) at an angle \(\alpha\) above the horizontal. The particles \(P\) and \(Q\) reach the ground at the same point and at the same time.

(b) Express \(V^2\) in the form \(kag\), where \(k\) is a rational number.