Find out a formula for the maximum height h which a rocket will reach if launched vertically from the surface of earth with speed v0 (< vesc). Deduce the terms of v0, rE, ME, and G.
i) Represent your answer in terms of the variable v0 and constants rE, ME, and G.
ii) Explain how high does a rocket go if 8.70 km/s? Avoid air resistance and the rotation of earth.