Work by gravity depends on vertical displacement

Steps:

• Weight W acts vertically downward with magnitude W.
• Displacement from top to bottom includes vertical drop h and horizontal component.
• Work done by W is ∫ F · ds = W * h, since only vertical component contributes (frictionless, no other forces affect this).
• Thus, work equals W times vertical height difference.

Why A is correct:

• A. Wx matches W times vertical displacement if x is the height h, per work-energy theorem where gravity's work is mgh = Wh.

Why the others are wrong:

• B. Wy: y likely horizontal distance; gravity does no work horizontally.
• C. W(y-z): y-z unclear but not purely vertical height; irrelevant to gravity's direction.
• D. W(x+z): x+z exceeds vertical height; overestimates work.

Final answer: A