A piece of a satellite falls to the ground from a height of \(10,000 \mathrm{~m}\). Ignoring air resistance, find the height as a function of time. [For free fall from large distances,

\[\ddot{h}=-\frac{G M}{(R+h)^{2}}\]

Multiplying both sides by \(\dot{h}\), show that

\[\frac{d}{d t}\left(\frac{1}{2} \dot{h}^{2}\right)=\frac{d}{d t}\left(\frac{G M}{R+h}\right)\]

Integrate and solve for \(\dot{h}\). Further integrating gives \(h(t)\).]