A particle \(P\) is projected from a point \(O\) on a horizontal plane and moves freely under gravity. The initial velocity of \(P\) is \(100 \mathrm{~ms}^{-1}\) at an angle \(\theta\) above the horizontal, where \(\tan \theta=\frac{4}{3}\). The two times at which \(P\) 's height above the plane is \(H \mathrm{~m}\) differ by 10 s .
(a) Find the value of \(H\).
(b) Find the magnitude and direction of the velocity of \(P\) one second before it strikes the plane.