Answer: Escape Velocity The minimum velocity required for an object to escape Earths

Chapter 5, Problem 60

(choose chapter or problem)

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

\(\int v d v=-G M \int \frac{1}{y^{2}} d y\)

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

\(v^{2}=v_{0}^{2}+2 G M\left(\frac{1}{y}-\frac{1}{R}\right)\)

where \(v_{0}\) is the initial velocity of the object and R is the radius of Earth.

Text Transcription:

int v d v=-G M \int \frac{1}{y^2 d y

v^{2}=v_{0}^{2}+2 G M(\frac{1}y-\frac{1}R)

v_{0}