Physics

Physics

Problem

An object is projected horizontally from a high tower on Earth with velocity vv. If vv is the orbital velocity for a grazing orbit, the object orbits the Earth. If the velocity is increased to 2v\sqrt{2}v, the object escapes. A satellite is currently orbiting at radius r=4Rr = 4R. What is the ratio of the escape velocity at this altitude to its current orbital velocity?

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