(i) Apply Newton's second law to the particles. For the 1.2 kg particle:

\(12 - T = 1.2a\)

For the 0.8 kg particle:

\(T - 8 = 0.8a\)

Solving these equations simultaneously gives:

\(a = 2 ext{ m/s}^2, \, T = 9.6 ext{ N}\)

(ii) First, find the time taken for the 1.2 kg particle to reach the ground:

\(0.64 = \frac{1}{2} \times 2 \times t_1^2\)

Solving gives:

\(t_1 = 0.8 ext{ s}\)

The speed of the 0.8 kg particle when the 1.2 kg particle hits the ground is:

\(v = 2 \times 0.8 = 1.6 ext{ m/s}\)

Next, find the time and distance for the 0.8 kg particle to come to rest:

\(0 = 1.6 - 10t_2\)

Solving gives:

\(t_2 = 0.16 ext{ s}\)

The distance travelled during this time is:

\(s_2 = \frac{1}{2} \times 1.6 \times 0.16 = 0.128 ext{ m}\)

Finally, find the distance travelled in the remaining time:

\(t_3 = 1 - 0.8 - 0.16 = 0.04 ext{ s}\)

\(s_3 = \frac{1}{2} \times 10 \times 0.04^2 = 0.008 ext{ m}\)

Total distance travelled:

\(0.64 + 0.128 + 0.008 = 0.776 ext{ m}\)