If each index card weighs the same, this means that gravity is pulling each card down with the same amount of force as it falls. Why, then, do some card designs fall slower when released from the same height?

The rate at which each card falls is related to the speed of the card. under gravity forces alone, the rate of increase of the speed of each card are equal. However, dur to drag (buoyancy) forces of air, the rate at which each card falls is dependent on its drag coefficient, which limit the maximum speed of falling of a card to a terminal velocity, , which is given as follows;

Where;

m = The mass of the card

g = The acceleration due to gravity ≈ 9.81 m/s²

ρ = The density of the air

A = The area the card projects, which depends on the card's shape

= The drag coefficient of the card

Therefore, due to the difference in the projected area, 'A', and the drag coefficient, , of each card, the terminal velocity of each index card will be different, and some card designs will fall slower than others when released from a given height

Explanation:

the closer the planet is to the sun, the larger the gravity