The image shows the original problem. Let me know if this is this is the answer to the problem that you wanted:
Remember that the mechanical energy [tex]E_m=E_k+E_p[/tex] of the system, (where [tex]E_k, E_p[/tex] are the kinetic energy and the potential energy respectively) must remain the same. In an initial situation, the athletes have purely kinetic energy. Then they hang on to the rope and reach a maximum height, at which point they have zero speed and thus zero kinetic energy. The athletes now have purely potential energy, remember again that the mechanical energy must be the same than it was initially, this implies that:
[tex]E_k=E_p\implies\frac{1}{2}mv^2=mgh_1\implies h_1=\frac{V^2}{2g}[/tex]
For the first athlete, and
[tex]E_k=E_p\implies\frac{1}{2}(2m)v^2=mgh_2\implies h_2=\frac{V^2}{g}[/tex]
for the second athlete.
We can see clearly that the second athlete rose higher than the first athlete.
