2. (15 points) A satellite is launched vertically from the pole of the Earth at the first cosmic speed. To what maximum distance from the Earth's surface will the satellite travel? (The acceleration due to gravity at the Earth's surface $g=10 \mathrm{m} / \mathrm{c}^{2}$, radius of the Earth $R=6400$ km).
2. 

According to the law of conservation of energy: $\frac{m v_{I}^{2}}{2}-\frac{\gamma m M}{R}=-\frac{\gamma m M}{R+H}$

The first cosmic speed $v_{I}=\sqrt{g R}$

The acceleration due to gravity at the surface $g=\frac{\gamma M}{R^{2}}$

Then $\frac{m g R}{2}-m g R=-\frac{m g R^{2}}{R+H}$

Finally, $H=R=6400$ km.

(15 points)