(i) Since the crate is lifted at constant speed, the tension in the cable equals the weight of the crate. The weight is given by:

\(W = mg\)

where \(m = 800 \text{ kg}\) and \(g = 10 \text{ m/s}^2\) (standard gravity approximation). Thus,

\(W = 800 \times 10 = 8000 \text{ N}\)

Alternatively, using \(g = 9.8 \text{ m/s}^2\) or \(g = 9.81 \text{ m/s}^2\), the tension can be \(7840 \text{ N}\) or \(7850 \text{ N}\) respectively.

(ii) The power applied is calculated using the formula:

\(P = \frac{\Delta W}{\Delta t}\)

where \(\Delta W = 800 \times 20\) (work done to lift the crate by 20 m) and \(\Delta t = 50 \text{ s}\).

\(\Delta W = 16000 \text{ J}\)

\(P = \frac{16000}{50} = 320 \text{ W}\)

Alternatively, using \(g = 9.8 \text{ m/s}^2\) or \(g = 9.81 \text{ m/s}^2\), the power can be \(3140 \text{ W}\).