Chapter 11.1, Problem 11.30P

The acceleration due to gravity of a particle falling toward the earth is $a=-g{R}^2/r^2$ , where r is the distance from the center of the earth to the particle, R is the radius of the earth, and g is the acceleration due to gravity at the surface of the earth. If $R=3960$ mi, calculate the escape velocity: that is, the minimum velocity with which a particle must be projected vertically upward from the surface of the earth if it is not to return to the earth. (Hint: $v=0$ for $r=\infty$ .)