# Free falling ball with and without air resistance

• xcortz
In summary, the conversation discusses a problem involving a 2 kg ball in free fall with an initial downward velocity of 12 m/s. The goal is to find the difference in displacement after 1s with and without air resistance, using various equations. The displacement without air resistance is calculated to be -16.9m, but the displacement with air resistance cannot be determined without a definition of the "k factor" for air resistance. Additionally, the given units for the k factor (0.02 m-1) are unusual and may not accurately represent air resistance.

## Homework Statement

A 2 kg ball (k factor of 0.02 m-1) is in free fall. The initial downward velocity of the ball is 12 m/s. Find the difference in displacement after 1s both with and without air resistance.

## Homework Equations

vf = vi + at
y = yi + 1/2(vi+vf)t
y - yi = vit + (1/2)At2 - (1/3)Bt3
F = ma

## The Attempt at a Solution

I have determined the displacement of the ball without air resistance to be -16.9m by first finding the final velocity after 1s:
vf = vi + at
= -12 + (-9.8)(1s)
= -21.8m/s

And then the final displacement:
y - yi = vit + (1/2)At2 - (1/3)Bt3
= 1/2(-12-21.8)(1s)
= -16.9m

However, I am unable to figure out how to find the displacement of the ball with air resistance present and how to incorporate the k factor. So far, I have determined:
F = (2kg)(-9.8)
= -19.6N

Not sure where to go from here :(

They need to define the "k factor" for the air resistance. That is not standard terminology, and it needs to be defined in order to proceed.

They need to define the "k factor" for the air resistance. That is not standard terminology, and it needs to be defined in order to proceed.
It also looks a little suspicious that the units for k are given as ##[m^{-1}]##, since generally air resistance is modeled as being proportional to either ##v## or the square of ##v##.

gneill said:
It also looks a little suspicious that the units for k are given as ##[m^{-1}]##, since generally air resistance is modeled as being proportional to either ##v## or the square of ##v##.
If we take the units on trust, for factor × something = force the something has to have units of energy. KE maybe? Weird.