The escape speed from Earth is vₑ. A body is projected from Earth's surface with speed 2vₑ. With what constant speed will it move far away in interplanetary space?
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The escape speed from Earth is vₑ. A body is projected from Earth's surface with speed 2vₑ. With what constant speed will it move far away in interplanetary space?

G1 Physics · Accepted Answer

At Earth's surface, vₑ² = 2GM/R. Energy conservation givₑ (1/2)m(2vₑ)² - GMm/R = (1/2)mv∞². Using GM/R = vₑ²/2 givₑ 2mvₑ² - (1/2)mvₑ² = (1/2)mv∞², so v∞² = 3vₑ² and v∞ = √3 vₑ. Correct answer: C.