To find the work done against resistance, we use the work-energy principle. The change in mechanical energy is equal to the work done against resistance.

The initial kinetic energy (KE) at the top is given by:

\(KE_{\text{top}} = \frac{1}{2} \times 15 \times 2^2 = 30 \text{ J}\)

The final kinetic energy (KE) at the bottom is:

\(KE_{\text{bottom}} = \frac{1}{2} \times 15 \times 4^2 = 120 \text{ J}\)

The change in potential energy (PE) as the block descends 1.6 m is:

\(\Delta PE = 15g \times 1.6 = 240 \text{ J}\)

According to the work-energy principle:

\(\Delta KE + \Delta PE = \text{Work done against resistance} + \text{Work done by gravity}\)

Substituting the values:

\(120 - 30 + 240 = 120 + W\)

Solving for \(W\):

\(240 + 30 = 120 + W\)

\(W = 150 \text{ J}\)