(i) The work done by the pulling force is calculated using the formula:

\(\text{Work Done} = Fd \cos \theta\)

Substituting the given values:

\(\text{Work Done} = 50 \times 20 \times \cos 10^{\circ} = 984.8 \text{ J}\)

(ii) Using the energy method, the work done by the driving force is equal to the kinetic energy gain plus the work done against resistance:

\(984.8 = \frac{1}{2} \times 25 \times v^2 + 30 \times 20\)

Solving for \(v\):

\(984.8 = 12.5v^2 + 600\)

\(384.8 = 12.5v^2\)

\(v^2 = 30.784\)

\(v = 5.55 \text{ ms}^{-1}\)

(iii) The greatest power is exerted when the speed is maximum:

\(\text{Power} = Fv\)

\(\text{Max Power} = 50 \cos 10^{\circ} \times 5.55 = 273 \text{ W}\)

(iv) Using Newton's second law up the plane:

\(50 \cos 10^{\circ} - 30 - 25g \sin 5^{\circ} = 25a\)

Solving for \(a\):

\(a = -0.102 \text{ ms}^{-2}\)

Using \(v = u + at\):

\(0 = 5.55 - 0.102t\)

\(t = \frac{5.55}{0.102} = 54.4 \text{ s}\)