First, apply Newton's second law along the direction of motion:

\(F - 1130 + 1250 \cdot g \cdot \sin(3^{\circ}) = 1250 \cdot 0.2\)

where \(F\) is the driving force, \(g\) is the acceleration due to gravity (approximately 9.8 m/s²).

Rearranging gives:

\(F = 1130 - 1250 \cdot g \cdot \sin(3^{\circ}) + 250\)

Next, use the power equation:

\(P = Fv\)

Given \(P = 22000\) W, substitute for \(F\):

\(22000 = (1130 - 1250 \cdot g \cdot \sin(3^{\circ}) + 250) \cdot v\)

Solve for \(v\):

\(v = \frac{22000}{725.8} \approx 30.3 \text{ m/s}\)