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## 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

_{i}t + (1/2)At

^{2}- (1/3)Bt

^{3}

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

_{i}t + (1/2)At

^{2}- (1/3)Bt

^{3}

= 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 :(