According to Newtons Law of Universal Gravitation, the gravitational force on an object

Chapter 9, Problem 44

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According to Newtons Law of Universal Gravitation, the gravitational force on an object of mass that has been projected vertically upward from Earths surface is where is the objects distance above the surface at time , is Earths radius, and is the acceleration due to gravity. Also, by Newtons Second Law, F ma mdvdt t R and so(a) Suppose a rocket is fired vertically upward with an initialvelocity . Let be the maximum height above the surfacereached by the object. Show that[Hint: By the Chain Rule, .](b) Calculate . This limit is called the escapevelocity for Earth.(c) Use mi and fts to calculate in feetper second and in miles per second.