Answer
The maximum height is $R_{max}/2$
Work Step by Step
A frog can reach its maximum vertical height if it jumps straight up with an initial speed of $v_0$.
We can find an expression for the maximum height $y_{max}$.
$2ay_{max} = v_0^2$
$y_{max} = \frac{v_0^2}{2g}$
Since the maximum range is $v_0^2/g$, we can see that the maximum height $y_{max}$ is $R_{max}/2$
