Air resistance

So far we have been ignoring air resistance, but it has a significant effect on the motion of objects in free fall (unless the object is in a vacuum). Air resistance acts similarly to friction, and it depends on four things:

• fluid density (air)
• surface area of cross section
• surface smoothness
• shape (aerodynamics)

In addition, air resistance is related to the moving object’s speed by

$\left|{\overrightarrow{F}}_{\text{air}}\right|\propto v^2\text{.}$

Because of air resistance, a falling object’s acceleration is actually less than 9.80 m/s², and it only gets smaller. Since air resistance increases in proportion to the square of speed, there reaches a point where the air resistance is equal and opposite to the gravitational force. Acceleration is now zero, so the object doesn’t gain any more speed. The velocity at this point is known as terminal velocity.

A skydiver might have a terminal velocity of around 200 km/h. When they open their parachute, terminal velocity decreases drastically.

Because of air resistance, objects of different mass actually can hit the ground at different times when dropped from a large enough height. All other things being equal, an object with more mass will have a greater terminal velocity.