A 4.6 kg rock is dropped from a clifftop and falls 7.1 m to the ground. How much momentum did it have just before it hit the ground? Give your answer to the nearest whole number.

Question

BlackTom AI · Accepted Answer

Use energy conservation to find the rock’s speed just before impact, then calculate momentum p = m v.

1) Relevant concepts
- Gravitational potential energy m g h converts to kinetic energy 1/2 m v^2 (neglecting air resistance).  
- Momentum p = m v.

2) Complete reasoning (step by step)
- Set m g h = 1/2 m v^2. Mass m cancels, so v = sqrt(2 g h).  
- Compute v, then compute p = m v.

3) Calculations with intermediate steps
- Given: m = 4.6 kg, h = 7.1 m, g = 9.8 m/s^2.  
- Compute 2 g h: 2 × 9.8 × 7.1 = 19.6 × 7.1 = 139.16.  
- v = sqrt(139.16) ≈ 11.803 m/s.  
- Momentum p = m v = 4.6 kg × 11.803 m/s = 54.2938 kg·m/s.  
- Rounded to the nearest whole number: p ≈ 54 kg·m/s.

4) Why this is correct
- Using energy conservation is valid because the only significant force doing work is gravity (air resistance neglected), so the drop’s loss in potential energy equals the gain in kinetic energy. Canceling m avoids needing the mass to find v, then multiplying by m yields the correct momentum. Numerical rounding gives the nearest whole-number momentum.

5) Other options
- This is a numerical question (no multiple-choice options provided). Any other numeric result would come from using a different g, rounding prematurely, or including air resistance; those were not specified.

6) Conclusion
- The computed momentum is approximately 54 kg·m/s, which matches the provided answer 54.

A 4.6 kg rock is dropped from a clifftop and falls 7.1 m to the ground. How much momentum did it have just before it hit the ground? Give your answer to the nearest whole number.Numerical

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