(Solved): Determine a formula for the maximum height h that a rocket will reach if launched vertically from ...

Determine a formula for the maximum height $$h$$ that a rocket will reach if launched vertically from the Earth's surface with speed $$v_0\left(<v_{\text{esc }}\right)$$. Express in terms of $$v_0,r_{\mathrm{E}},M_{\mathrm{E}}$$, and $$G$$. Express your answer in terms of the variable $$v_0$$ and constants $$r_{\mathrm{E}},M_{\mathrm{E}}$$, and $$G$$. Part B How high does a rocket go if $$8.50\mathrm{km}/\mathrm{s}$$ ? Ignore air resistance and the Earth's rotation.