Work-energy theorem

Steps:

• Calculate initial kinetic energy: $\frac{1}{2} \times 1.2 \, \text{kg} \times (3.0 \, \text{m/s})^2 = 5.4 \, \text{J}$.
• Final kinetic energy is 0 J since the ball stops.
• Change in kinetic energy $\Delta KE = 0 - 5.4 = -5.4 \, \text{J}$.
• Work done by cushion equals $\Delta KE$, so magnitude is 5.4 J (distance not needed for total work).

Why C is correct:

• Matches initial kinetic energy, which the cushion dissipates per work-energy theorem.

Why the others are wrong:

• A: Incorrect; possibly miscalculates as $m v d = 1.2 \times 3 \times 0.2 / 3$, but irrelevant.
• B: Incorrect; equals $\frac{1}{2} m v = 1.8 \, \text{J}$, confusing momentum with energy.

Final answer: C