Concept:Using the Law of Conservation of Energy, the loss in potential energy equals the gain in kinetic energy. The velocity depends only on the distance it has
fallen, not the mass.
Formula:$$ v = \sqrt{2g\Delta h} $$
Solution:- Initial height = 5.0 m
- Final height = 3.0 m
- Distance fallen (\( \Delta h \)) = 5.0 - 3.0 = 2.0 m
- \( v = \sqrt{2 \times 9.8 \times 2.0} = \sqrt{39.2} \)
- Since \( 6^2 = 36 \) and \( 7^2 = 49 \), \( \sqrt{39.2} \) is slightly more than 6.
- \( v \approx 6.26 \text{ m/s} \), which rounds to 6.3 m/s.
Why other options are incorrect:Using the remaining height (3m) instead of the fallen distance gives \( \sqrt{2 \times 9.8 \times 3} \approx 7.7 \text{ m/s} \). Calculating velocity at the very bottom (h=5m) gives \( \sqrt{98} \approx 9.9 \text{ m/s} \).
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