(i) Resolve the forces horizontally and vertically:

Horizontal: \(F \cos 70^\circ + 20 - 10 \cos 30^\circ = R \cos 15^\circ\)

Vertical: \(10 \sin 30^\circ - F \sin 70^\circ = R \sin 15^\circ\)

Solving these equations simultaneously gives \(F = 1.90 \text{ N}\) and \(R = 12.4 \text{ N}\).

(ii) Use the equation of motion: \(v^2 = u^2 + 2as\)

\(11.7^2 = 0 + 2a \times 3\)

\(a = 22.815 \text{ m/s}^2\)

Applying Newton's second law: \(R \cos 15^\circ = m \times 22.815\)

\(m = \frac{R \cos 15^\circ}{22.815} = 0.526 \text{ kg}\)