An object is projected vertically up from the earth's surface with velocity Rg where R is the radius of the earth and ' g ' is the acceleration due to earth on the surface of earth. T

Question

An object is projected vertically up from the earth's surface with velocity Rg ​ where R is the radius of the earth and ' g ' is the acceleration due to earth on the surface of earth. The maximum height reached by the object.

TestHub · Accepted Answer

Let the object of mass m projected with speed u = g R ​ reach a height ' h ' above surface of earth. Then from conservation of energy 2 1 ​ m u 2 − R GM m ​ = − R + h GM m ​ ​ u 2 = g R = R GM ​ ⇒ ​ 2 1 ​ R GM m ​ − R GM m ​ = − R + h GM m ​ or h = R ​

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