Answer
\[ v_{\text{max}} = v_{\text{min}} \frac{1-e}{1+e} \]
Work Step by Step
As stated in the exercise, we use the previous results. This is a simple matter of plugging things into the formula so we easily see that: \[ v_{\text{max}} = \frac{r_{\text{max}}}{r_{\text{min}}} v_{\text{min}} = \frac{a(1+e)}{a(1-e)}v_{\text{min}} = v_{\text{min}} \frac{1+e}{1-e} \] Result: \[ v_{\text{max}} = v_{\text{min}} \frac{1+e}{1-e} \]
