Answer
1.3 m.
Work Step by Step
Jane’s mechanical energy is conserved. Take y = 0 at the bottom. The initial KE + initial PE equals the final KE + final PE. She comes to a momentary stop at the end.
$$\frac{1}{2}mv_i^2 + mgy_i=\frac{1}{2}mv_f^2 + mgy_f $$
$$\frac{1}{2}mv_i^2 + 0 = 0 + mgy_f $$
$$y_f=\frac{v_i^2}{2g}=1.3 m$$
The vine length does not matter as long as it is longer than about 0.65 m so that she can rise 1.3 m.
