(i) For \(P_1\), using \(s = ut - \frac{1}{2}gt^2\), we have:

\(25 = 30t - 5t^2\)

Solving \(5t^2 - 30t + 25 = 0\) gives \((t-1)(t-5) = 0\), so \(t = 1\) or \(t = 5\).

Thus, \(P_1\) is higher than the tower for \(1 < t < 5\).

(ii) For \(P_1\) and \(P_2\), using \(s_1 = 30t - 5t^2\) and \(s_2 = 10t - 5t^2\), and \(s_1 = s_2 + 25\):

\(30t - 10t = 25\)

\(t = 1.25\)

Velocities: \(v_1 = 30 - 10 \times 1.25 = 17.5\) m s\(^{-1}\), \(v_2 = 10 - 10 \times 1.25 = -2.5\) m s\(^{-1}\).

(iii) Using \(t_{up} = 3\) and \(t_{equal} = 1.25\), the time is \(1.75\) s or \(1.25 < t < 3\).