# How does the air resistance affects the graph of a free falling body?

##### 1 Answer

See explanation

#### Explanation:

The differential equation of the free fall with air resistance is :

with

m = mass of falling object

g = gravity constant = 10 m/s² (9.81 but we take 10 for simplicity)

c = constant depending on the Cx value of the object among others

v = vertical velocity downwards of the falling object in m/s

The solution is

with

and

If we take

we get

with h the height fallen, measured downwards.

We have to compare this with the frictionless fall :

Clearly the latter is a parabole, while the former is flatter.

For the rest there is not much to see about the graphics, but i have added a graph anyway (the red line is frictionless fall, the yellow with air resistance) :