At height \(3 R\), i.e at distance \(4 R\) from the centre of the earth,

\(V_{\text {orbital }}=\sqrt{\frac{G M}{r}}\)

Here, \(r=4 R \Rightarrow V_0=\sqrt{\frac{G M}{4 R}}=\frac{1}{2} \sqrt{\frac{G M}{R}}\),

Thus, an object taken to a height \(3 R\) if projected horizontally with speed \(\frac{1}{2} \sqrt{\frac{G M}{R}}\), will start rotating around earth in a circular orbit.