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Near Earth’s surface, gravity is approximately constant (F = mg), and the force acts vertically. Thus, work (W = F⋅Δh) depends only on vertical displacement (Δh), as horizontal motion is perpendicular to the force.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
The work done by gravity is independent of the path taken and depends only on the initial and final positions. This path independence defines a conservative force, allowing a potential energy function to be defined.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.
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