First, calculate the maximum height reached by the particle. Using the equation for upward motion:

\(0 = u^2 - 2gs\)

where \(u = 9 \text{ m/s}\) and \(g = 9.8 \text{ m/s}^2\). Solving for \(s\):

\(0 = 9^2 - 2 \times 9.8 \times s\)

\(s = \frac{81}{19.6} = 4.05 \text{ m}\)

The total distance travelled is the sum of the distance upwards and downwards:

\(\text{Total distance} = 4.05 + (3.15 + 4.05) = 11.25 \text{ m}\)

Next, calculate the time taken to reach the maximum height:

\(v = u - gt\)

Setting \(v = 0\):

\(0 = 9 - 9.8t\)

\(t = \frac{9}{9.8} = 0.9 \text{ s}\)

For the downward motion, use:

\(s = \frac{1}{2} gt^2\)

where \(s = 3.15 + 4.05 = 7.2 \text{ m}\):

\(7.2 = \frac{1}{2} \times 9.8 \times t^2\)

\(t^2 = \frac{14.4}{9.8}\)

\(t = 1.2 \text{ s}\)

The total time taken is:

\(\text{Total time} = 0.9 + 1.2 = 2.1 \text{ s}\)