Answer: 19.4 km/s.
- A 22.4 km/s
- B 11.2 km/s
- C 19.4 km/s
- D 33.6 km/s
Correct answer: C. 19.4 km/s
Explanation: Energy conservation: v<sub>∞</sub> = √(v<sup>2</sup> - v<sub>e</sub><sup>2</sup>) = √(22.4<sup>2</sup> - 11.2<sup>2</sup>) = √376.3 ≈ 19.4 km/s.
g is maximum at Earth's surface; going up, it falls off as 1/r² (inverse-square); going down, it falls off linearly with depth (since only the mass enclosed within radius r contributes), reaching zero at the centre.
Concept context
Universal gravitation, orbital mechanics, gravitational potential, and escape velocity.