First, calculate the gravitational potential energy (PE) lost by the particle:

\(\text{Loss of PE} = mgh = 1.6 \times 9.8 \times 9 = 144 \text{ J}\)

Next, calculate the kinetic energy (KE) gained by the particle just before hitting the ground:

\(\text{KE} = \frac{1}{2}mv^2 = \frac{1}{2} \times 1.6 \times 12^2 = 115.2 \text{ J}\)

The work done against air resistance (WD) is the difference between the loss of potential energy and the gain in kinetic energy:

\(\text{WD} = \text{Loss of PE} - \text{KE} = 144 - 115.2 = 28.8 \text{ J}\)