(i) The kinetic energy (KE) gained by the particle at B is given by:

\(KE = \frac{1}{2} \times 0.15 \times 8^2\)

\(KE = 4.8 \text{ J}\)

Since there are no resistances, the potential energy (PE) lost is equal to the kinetic energy gained:

\(mgh = KE\)

\(0.15 \times 9.8 \times h = 4.8\)

\(h = \frac{4.8}{0.15 \times 9.8}\)

\(h = 3.2 \text{ m}\)

(ii) The work done against resistances is the difference between the potential energy lost and the kinetic energy gained:

\(WD = mgh - \frac{1}{2} mv^2\)

\(WD = 0.15 \times 9.8 \times 4 - \frac{1}{2} \times 0.15 \times 6^2\)

\(WD = 5.88 - 2.7\)

\(WD = 3.18 \text{ J}\)

Rounding to one decimal place, the work done is 3.3 J.