Gravitational Potential Energy Depends on Vertical Height

Steps:

• Gravitational potential energy (U) is given by U = mgh, where h is the vertical height above a reference level.
• Horizontal displacement changes the object's x-position but not its vertical height h.
• In a uniform vertical gravitational field, the field acts only downward, unaffected by horizontal motion.
• Thus, U remains constant regardless of horizontal displacement.

Why B is correct:

• U = mgh depends solely on height; horizontal displacement leaves h unchanged, so U does not change.

Why the others are wrong:

• A: Decrease would require lowering height, but horizontal motion does not alter h.
• C: Increase would need rising height, which horizontal displacement does not cause.
• D: Squared relation applies to kinetic energy in free fall, not potential energy here.

Final answer: B