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title: "A rocket of mass \\( m \\) is launched with kinetic energy \\( K_0 \\), from the surface of the Earth. How much less kinetic energy does the rocket have at an altitude of two Earth radii? Give your answer in terms of the gravitational constant \\( G \\), the mass of the Earth \\( m_E \\), the radius of the Earth \\( R_E \\), and the mass of the rocket?"
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url: "https://nerd-notes.com/ubq/22709/"
date_modified: "2025-04-18T02:58:36+00:00"
---

# A rocket of mass \( m \) is launched with kinetic energy \( K_0 \), from the surface of the Earth. How much less kinetic energy does the rocket have at an altitude of two Earth radii? Give your answer in terms of the gravitational constant \( G \), the mass of the Earth \( m_E \), the radius of the Earth \( R_E \), and the mass of the rocket?

A rocket of mass \( m \) is launched with kinetic energy \( K_0 \), from the surface of the Earth. How much less kinetic energy does the rocket have at an altitude of two Earth radii? Give your answer in terms of the gravitational constant \( G \), the mass of the Earth \( m_E \), the radius of the Earth \( R_E \), and the mass of the rocket?

- **A.** \[\dfrac{GM_{E}m}{2R_{E}} \]
- **B.** \[ \dfrac{2GM_{E}m}{3R_{E}} \]
- **C.** \[ \dfrac{3GM_{E}m}{4R_{E}} \]
- **D.** \[\dfrac{8GM_{E}m}{9R_{E}} \]
- **E.** More information is needed.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/22709/*