Resolve forces perpendicular to the rod:

\(8 \sin 10^{\circ} + R = 0.3g\)

Solving for \(R\):

\(R = 0.3g - 8 \sin 10^{\circ} \approx 2.943 - 1.388 = 1.555 \text{ N}\)

Resolve forces along the rod:

\(8 \cos 10^{\circ} - F = 0.3a\)

Using friction \(F = \mu R\):

\(F = 0.8 \times 1.555 \approx 1.244 \text{ N}\)

Substitute \(F\) into the equation:

\(8 \cos 10^{\circ} - 1.244 = 0.3a\)

Calculate \(a\):

\(a = \frac{8 \cos 10^{\circ} - 1.244}{0.3} \approx \frac{7.878 - 1.244}{0.3} \approx 21.966 \text{ m/s}^2\)

Use the equation of motion:

\(s = ut + \frac{1}{2}at^2\)

Given \(s = 0.6 \text{ m}, u = 0\):

\(0.6 = \frac{1}{2} \times 21.966 \times t^2\)

Solve for \(t\):

\(t^2 = \frac{0.6}{10.983} \approx 0.0546\)

\(t = \sqrt{0.0546} \approx 0.234 \text{ seconds}\)