(i) Using the formula for power, \(P = Fv\), where \(P = 36000\) W and \(F = 800\) N, we have:
\(36000 = 800v\)
\(v = \frac{36000}{800} = 45 \text{ m/s}\)
The distance \(AB\) is given by \(v \times t = 45 \times 120 = 5400 \text{ m}\).
(ii) Using Newton's second law, \(-800 = 900a\), we find \(a = -\frac{8}{9} \text{ m/s}^2\).
Using the equation \(v^2 = u^2 + 2as\), where \(u = 45 \text{ m/s}\), \(s = 450 \text{ m}\):
\(v^2 = 45^2 - \frac{16}{9} \times 450\)
\(v = 35 \text{ m/s}\)
(iii) The distance \(CD = 6637.5 - 5400 - 450 = 787.5 \text{ m}\).
Using \(v^2 = u^2 + 2as\), where \(u = 35 \text{ m/s}\), \(v = 0\):
\(0 = 35^2 - 2d \times 787.5\)
\(d = \frac{7}{9} = 0.778 \text{ m/s}^2\)
Using \(F = ma\), \(R = 900 \times \frac{7}{9} = 700 \text{ N}\).