Concept:According to the Conservation of Energy in the presence of non-conservative forces, the initial potential energy is converted into kinetic energy plus the work done against friction.
Formula:$$ E_{\text{initial}} = E_{\text{final}} + W_{\text{friction}} $$
Solution:- Initial energy at height \( h \) is entirely Potential Energy: \( P.E = mgh \)
- Final energy at the bottom is Kinetic Energy: \( K.E = \frac{1}{2}mv^2 \)
- Work done against air friction over distance \( h \): \( W = fh \)
- Equating them: \( mgh = \frac{1}{2}mv^2 + fh \)
Why other options are incorrect:Option A implies energy is created. Option B implies friction work equals total energy. Option C incorrectly subtracts friction work instead of adding it to the final state energies.
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