A rocket is to be shot radially outward from Earth's surface. Neglecting Earth's rotation, find the radial distance from Earth's center that the rocket reaches if it is launched with (a) 0.400 times the escape speed from Earth and (b) 0.400 times the kinetic energy that is required to escape Earth. (c) At launch, what is the least mechanical energy required for it to escape Earth ?

Explanation

(a) `7.58 xx 10^6 N`, (b) `1.06 xx 10^7m`,( c )The mechanical energy is zero for the "escape condition."