Question

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 above the ground. later, a 100 kg athlete, running at the same speed, grabs a similar rope hanging from a 5-meter-high platform. what is the maximum height to which the 100 kg athlete swings?

Answer 1

The answer is: 1.8 meters.

Explanation:
An athlete swinging can be considered a pendulum.

The pendulum's maximum height is the point at which it changes direction, which means that its velocity is equal to zero. In this point, for the mechanical energy conservation, all its kinetic energy is transformed into potential energy. Similarly, when the pendulum is at its resting position (when the athlete grabs the rope), its energy is totally kinetic.

Therefore we can say that:
$\frac{1}{2}m v_{1} ^{2} = mgh_{max}$

Solving for h:
$h_{max} = \frac{v^{2}}{g}$

As we can see, the maximum height is independent on the mass and on the length of the rope, therefore it will be the same for the 100kg-athlete as it is for the 50kg-athlete, since their initial speeds are the same.

We know that the 50kg-athlete reached a height of 1.8 m, hence, the maximum height reached by the 100kg-athlete will be 1.8 m.