An athlete with mass m running at speed v grabs a light rope that hangs from a ceiling of height H and swings to a maximum height of h1. In another room with a lower ceiling of height H/2 , a second athlete with mass 2m running at the same speed v grabs a light rope hanging from the ceiling and swings to a maximum height of h2 . How does the maximum height reached by the two athletes compare, and why

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:

Athlete B:

Both athletes reach the same height, as maximum height is a function independent of the mass, but dependent on initial speed and gravity constant.