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

Substitute \(u = 3 \text{ m/s}, a = 2.5 \text{ m/s}^2, s = 8 \text{ m}\).

\(v^2 = 3^2 + 2 \times 2.5 \times 8\)

\(v^2 = 9 + 40 = 49\)

\(v = 7 \text{ m/s}\)

(ii) Kinetic energy gain: \(\frac{1}{2} \times 0.8 \times (7^2 - 3^2) = 16 \text{ J}\)

Potential energy loss: \(16 + 7 = 23 \text{ J}\)

\(0.8 \times 10 \times 8 \sin \alpha = 23\)

\(\sin \alpha = \frac{23}{64}\)

\(\alpha = 21.1^\circ \text{ or } 0.368 \text{ radians}\)

(iii) Average speed \(= \frac{3 + 7}{2} = 5 \text{ m/s}\)

Use \(v^2 = u^2 + 2as\) for point X: \(5^2 = 3^2 + 2 \times 2.5 \times s\)

\(25 = 9 + 5s\)

\(s = 3.2 \text{ m}\)

Work done \(= \frac{7}{8} \times 3.2 = 2.8 \text{ J}\)