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Evidently, there are formulas that allow us to represent the effect of air resistance on the velocity of an object in free fall but how would one calculate the effect of air resistance on horizontal motion, for instance how much air resistance hinders a humans speed or so ?

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Nothing on how to think about air resistance depends on the direction you move into. Same usual representations applying to a free fall are used for other purposes. Mainly a force that is $\sim\vec v$ in case of a laminar regime or $\sim|\vec v|^2 \hat v$ in a turbulent one.

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