Free falling ball with and without air resistance

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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


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 :(
 

Answers and Replies

  • #2
Charles Link
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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.
 
  • #3
gneill
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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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  • #4
haruspex
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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.
 
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