Question

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?

Answer 1

because KE is 1/2 m v^2, and PE is mgh2
then h2 depends on v^2 because the masses are the same before and after.
so h2 = 1/2 v^2/g in both cases, so h2 is independent of mass, or the original height of the ceiling.

Answer 2

v = sqrt (2gh)
h depends only on v (on earth anyway)