Answer:
Same height, height does not depend on mass, but on initial speed and gravity constant.
Step-by-step explanation:
It is assumed that each athlete begin at a height of zero. The physical model of each athlete is derived of application of the Principle of Energy Conservation:
Athlete A:
[tex]\frac{1}{2}\cdot m \cdot v^{2} = m \cdot g \cdot h_{1}\\\frac{1}{2}\cdot v^{2} = g \cdot h_{1}\\h_{1} = \frac{1}{2}\cdot \frac{v^{2}}{g}[/tex]
Athlete B:
[tex]\frac{1}{2}\cdot (2\cdot m) \cdot v^{2} = (2\cdot m) \cdot g \cdot h_{2}\\\frac{1}{2}\cdot v^{2} = g \cdot h_{2}\\h_{2} = \frac{1}{2}\cdot \frac{v^{2}}{g}[/tex]
Both athletes reach the same height, as maximum height is a function independent of the mass, but dependent on initial speed and gravity constant.
