Work done against resistance equals loss in mechanical energy

Steps:

• Compute initial kinetic energy: $\frac{1}{2} m v^2 = \frac{1}{2} \times 0.8 \times 8^2$.
• Compute gain in gravitational potential energy: $m g h = 0.8 \times 10 \times 1.5$.
• Apply work-energy theorem: work against resistance = initial KE - PE gain (energy dissipated by non-conservative force).
• Result: 0.4 J.

Why A is correct:

• Matches the mechanical energy loss via work-energy theorem, where non-conservative work = $\Delta$KE + $\Delta$PE = -initial KE + mgh.

Why the others are wrong:

• B. Overestimates dissipation by confusing with partial PE gain.
• C. Misapplies formula, possibly averaging energies incorrectly.
• D. Confuses with full initial KE or unrelated total energy.

Final answer: A