Question: The minimum velocity required for an object to escape Earths gravitational pull is obtained from the solution of the equation where v is the velocity

The minimum velocity required for an object to escape Earth’s gravitational pull is obtained from the solution of the equation

[v dv= 11/2 v dv = - GM dy

where v is the velocity of the object projected from Earth, y is the distance from the center of Earth, G is the gravitational constant, and M is the mass of Earth. Show that v and y are related by the equation

where v₀ is the initial velocity of the object and R is the radius of Earth.

[v dv= 11/2 v dv = - GM dy

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