Halliday, Resnick & Walker — Gravitation: Problem Problem_40

A projectile is shot directly away from Earth’s surface. Neglect the rotation of Earth. What multiple of Earth’s radius \(R_E\) gives the radial distance a projectile reaches if (a) its initial speed is \(0.500\) of the escape speed from Earth and (b) its initial kinetic energy is \(0.500\) of the kinetic energy required to escape Earth? (c) What is the least initial mechanical energy required at launch if the projectile is to escape Earth?