(i) The gain in gravitational potential energy (GPE) is given by \(mgh\), where \(m = 16000 \text{ kg}\), \(g = 10 \text{ m s}^{-2}\), and \(h = 20 \text{ m}\). Thus, \(\text{GPE} = 16000 \times 10 \times 20 = 3.2 \times 10^6 \text{ J}\).

(ii) The work done by the driving force is \(\text{force} \times \text{distance} = 5000 \times 1000 = 5 \times 10^6 \text{ J}\).

(iii) The work done against the force resisting the motion is the difference between the work done by the driving force and the gain in GPE: \(5 \times 10^6 - 3.2 \times 10^6 = 1.8 \times 10^6 \text{ J}\).

(iv) The increase in kinetic energy (KE) is \(\frac{1}{2} m (v^2 - u^2)\), where \(m = 16000 \text{ kg}\), \(u = 10 \text{ m s}^{-1}\), and \(v = 25 \text{ m s}^{-1}\). Thus, \(\text{increase in KE} = \frac{1}{2} \times 16000 \times (25^2 - 10^2) = 4.2 \times 10^6 \text{ J}\).

The work done against resistance is \(1500 \times 2000 = 3 \times 10^6 \text{ J}\).

The total work done by the driving force is the sum of the increase in KE and the work done against resistance: \(4.2 \times 10^6 + 3 \times 10^6 = 7.2 \times 10^6 \text{ J}\).