# Free falling ball with and without 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 :(

Homework Helper
Gold Member
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.

gneill
Mentor
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##.

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