(a) The forward force exerted by the cyclist's driving force is given by \(\frac{180}{6} = 30 \text{ N}\).

Using Newton's second law, the equation of motion is:

\(30 - F - 70g \sin \alpha = 70 \times (-0.2)\)

Substitute \(g = 9.8 \text{ m s}^{-2}\) and \(\sin \alpha = 0.05\):

\(30 - F - 70 \times 9.8 \times 0.05 = 70 \times (-0.2)\)

\(30 - F - 34.3 = -14\)

\(F = 9 \text{ N}\)

(b) For steady speed, acceleration \(a = 0\). Using the power equation:

\(\frac{180}{v} - F - 70g \sin \alpha = 0\)

Substitute \(F = 9 \text{ N}\) and \(\sin \alpha = 0.05\):

\(\frac{180}{v} - 9 - 34.3 = 0\)

\(\frac{180}{v} = 43.3\)

\(v = \frac{180}{43.3} \approx 4.09 \text{ m s}^{-1}\)