A 50 kg athlete running at speed v grabs a light rope that hangs from a 10-meter-high platform and swings to a maximum of 1.8 m
1 answer:
The solution is: 1.8 meters.
Explanation:
An athlete swinging on a rope can be modeled as a pendulum.
The pendulum attains its highest point—the moment it reverses direction—where its velocity drops to zero. At this apex, due to conservation of mechanical energy, its kinetic energy is completely converted to potential energy. Conversely, at the bottom position where the athlete holds the rope, all energy is purely kinetic.
Therefore, we can write:
Solving for height (h):
It’s clear that the maximum height depends neither on the rope’s length nor the mass of the athlete, implying the 100kg athlete starting with the same initial speed will reach the same maximum height as the 50kg athlete.
Since the 50kg athlete swings to a height of 1.8 m, the 100kg athlete’s maximum height will also be 1.8 m.
Explanation:
An athlete swinging on a rope can be modeled as a pendulum.
The pendulum attains its highest point—the moment it reverses direction—where its velocity drops to zero. At this apex, due to conservation of mechanical energy, its kinetic energy is completely converted to potential energy. Conversely, at the bottom position where the athlete holds the rope, all energy is purely kinetic.
Therefore, we can write:
Solving for height (h):
It’s clear that the maximum height depends neither on the rope’s length nor the mass of the athlete, implying the 100kg athlete starting with the same initial speed will reach the same maximum height as the 50kg athlete.
Since the 50kg athlete swings to a height of 1.8 m, the 100kg athlete’s maximum height will also be 1.8 m.
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