We start by using the principle of conservation of energy. The loss in potential energy (PE) is equal to the gain in kinetic energy (KE) plus the work done (WD) against resistance.

The change in kinetic energy is given by:

\(\text{Change in KE} = \frac{1}{2} m (v^2 - u^2)\)

where \(m = 8 \text{ kg}\), \(v = 8 \text{ m/s}\), and \(u = 3 \text{ m/s}\).

\(\text{Change in KE} = \frac{1}{2} \times 8 \times (8^2 - 3^2) = \frac{1}{2} \times 8 \times (64 - 9) = \frac{1}{2} \times 8 \times 55 = 220 \text{ J}\)

The work done against resistance is 120 J, so the total energy change is:

\(\text{Total energy change} = 220 + 120 = 340 \text{ J}\)

The loss in potential energy is given by:

\(\text{PE loss} = mgh\)

where \(g = 9.8 \text{ m/s}^2\) and \(h\) is the height.

\(340 = 8 \times 9.8 \times h\)

\(h = \frac{340}{8 \times 9.8} = \frac{340}{78.4} \approx 4.25 \text{ m}\)

Therefore, the height of the top of the plane above the level of the bottom is 4.25 m.