Free falling ball with and without air resistance

[xcortz]

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

v_f = v_i + at
y = y_i + 1/2(v_i+v_f)t
y - y_i = v_it + (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:
v_f = v_i + at
= -12 + (-9.8)(1s)
= -21.8m/s

And then the final displacement:
y - y_i = v_it + (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 :(

 

[Charles Link]

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]

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 $v$.

 

[haruspex]

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.