Physics

Problem

Calculate the escape speed from Earth’s surface. Take

g=9.8\,\text{m s}^{-2}

and Earth’s mean radius

R=6.4\times10^{6}\,\text{m}

. a)

12.8\,\text{km s}^{-1}

10.8\,\text{km s}^{-1}

11.2\,\text{km s}^{-1}

7.9\,\text{km s}^{-1}

Intuitive explanation

Escape speed is the minimum velocity needed to break free from a planet's gravitational pull with no further propulsion. The key insight is to use energy conservation: set the kinetic energy at Earth's surface equal to the gravitational potential energy you must overcome to reach infinity. This avoids messy calculus and gives you a clean formula relating $g$ , $R$ , and the speed you're solving for.

Intuitive explanation

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