(i) To find the greatest height above the ground, use the equation of motion:

\(0 = 5.2^2 - 2 imes 10.4 imes s_1\)

\(s_1 = \frac{5.2^2}{2 imes 10.4} = 1.3 ext{ m}\)

The total height above the ground is:

\(6.2 + 1.3 = 7.5 ext{ m}\)

(ii) To find the speed with which P reaches the ground, use the equation:

\(v^2 = 2 imes 9.6 imes 7.5\)

\(v = \sqrt{2 imes 9.6 imes 7.5} = 12 ext{ m/s}\)

(iii) To find the total work done by the air resistance, calculate the energy changes:

\(Potential energy loss = 0.6 imes 9.8 imes 6.2 = 37.2 ext{ J}\)

\(Initial total energy = 0.6 imes 9.8 imes 6.2 + \frac{1}{2} imes 0.6 imes 5.2^2 = 45.312 ext{ J}\)

\(Energy loss upward = \frac{1}{2} imes 0.6 imes 5.2^2 - 0.6 imes 9.8 imes 1.3 = 0.312 ext{ J}\)

\(Kinetic energy gain = \frac{1}{2} imes 0.6 imes 12^2 = 43.2 ext{ J}\)

\(Energy loss downward = -\frac{1}{2} imes 0.6 imes 12^2 + 0.6 imes 9.8 imes 7.5 = -1.8 ext{ J}\)

\(Total work done = 37.2 - 35.088 + 45.312 - 43.2 = 2.11 ext{ J}\)