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 heigh
t 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.
Both equations have the same slope, but are separated by virtue of their different values of b, the y-intercept. The same slope means they are parallel lines. Since the y-intercept is different, they do not overlap.
As they say, "Parallel line have a lot in common. Too bad they'll never meet."