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Imagine an asteroid starting to move toward the Earth from an infinitely far distance and from...

Imagine an asteroid starting to move toward the Earth from an infinitely far distance and from rest. The speed of the asteroid when it reaches to a distance ? from the center of the Earth is ?1. It will have a speed of ?2 after it travels more and reaches to a distance ?/2from the center of the Earth. What is the ratio of ?2 and ?1? Prove your answer.

Hint: Use work-kinetic energy theorem

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