Work equals gravitational potential energy change on frictionless incline

Steps:

• Since the plank is frictionless, minimum work done equals the gain in gravitational potential energy, mgh.
• Use m = 50 kg, g = 9.8 m/s², h = 1.6 m (vertical height; path length irrelevant).
• Calculate: 50 × 9.8 × 1.6 = 784 J, which rounds to 780 J.
• The 3.4 m plank length affects angle but not total work against gravity.

Why C is correct:

• 780 J matches the formula W = mgh for potential energy increase.

Why the others are wrong:

• A: Underestimates by using incorrect g or height (e.g., 50 × 1.6 × 1 = 80 J).
• B: Likely misapplies height as half or uses plank length fraction (e.g., 50 × 9.8 × 0.34 ≈ 170 J).
• D: Overestimates by including work along full plank (e.g., mgh with doubled height or friction assumption).

Final answer: C