Solution: According to Newtons Law of Universal Gravitation, the gravitational force on

Chapter 7, Problem 54

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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 the earths surface is F mtR2 x R2where is the objects distance above the surface at time , is the earths radius, and is the acceleration due to gravity. Also, by Newtons Second Law, and som dv dt mtR2 x R2(a) Suppose a rocket is red vertically upward with an initial velocity . Let be the maximum height above the surface reached by the object. Show thatv0 2tRh R h c [Hint: By the Chain Rule, .] (b) Calculate . This limit is called the escape velocity for the earth. (c) Use mi and fts to calculate in feet per second and in miles per second.

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