To analyze the kinetic energy of the feather as it reaches the ground, let's follow these steps:
1. Determine the potential energy at the initial height:
The potential energy (PE) of an object at a certain height is given by the formula:
[tex]\[
PE = m \cdot g \cdot h
\][/tex]
where:
- [tex]\( m = 0.001 \)[/tex] kg (mass of the feather)
- [tex]\( g = 9.8 \)[/tex] m/s² (acceleration due to gravity)
- [tex]\( h = 2 \)[/tex] m (height)
Substituting the values, we get:
[tex]\[
PE = 0.001 \times 9.8 \times 2 = 0.0196 \, \text{J}
\][/tex]
So, the potential energy at the height of 2 meters is 0.0196 joules.
2. Convert potential energy to kinetic energy:
Under ideal conditions (i.e., in the absence of any air resistance or other forces), the potential energy of the feather would be entirely converted into kinetic energy (KE) as it falls. Therefore, the maximum theoretical kinetic energy would be:
[tex]\[
KE_{\text{max\_theoretical}} = PE = 0.0196 \, \text{J}
\][/tex]
3. Consider the effect of air resistance:
In realistic conditions, the feather experiences air resistance as it falls. Air resistance is a force that opposes the motion of an object through air. Because of this resistance, some of the potential energy is used to overcome air resistance and is not fully converted into kinetic energy. This means that the actual kinetic energy of the feather as it reaches the ground will be less than the maximum theoretical value.
4. Conclusion:
Given that some of the potential energy is lost to air resistance, the kinetic energy of the feather when it reaches the ground will be less than the initially calculated potential energy of 0.0196 joules.
Therefore, the correct answer is:
[tex]\[
\boxed{B \, KE < 0.0196 \, \text{J}}
\][/tex]
