Solution:

The velocity required to reach a height equal to the Earth's radius \( R \) is the escape velocity for a total distance of \( 2R \) from the Earth's center.

Escape velocity formula:

\[
v = \sqrt{\frac{GM}{R}}
\]

At height \( h = R \), the velocity needed is:

\[
v = \sqrt{\frac{GM}{2R}} = \frac{V_e}{\sqrt{2}}
\]

Thus, the velocity is:

\[
v = \frac{V_e}{\sqrt{2}} = \frac{\sqrt{2GM/R}}{\sqrt{2}} = \sqrt{\frac{GM}{R}} = V_e/\sqrt{2}= \sqrt{\frac{GM}{R}}
\]