In the rope climb, a 75 kg athlete climbs a vertical distance of 5.0 m in 9.0 s. What minimum power output was used to accomplish this feat? ___ W

The minimum power output used to accomplish this feat is 408.625 watts.

Step-by-step explanation:

The minimum power is that needed to overcome potential gravitational energy at constant velocity. From Principle of Energy Conservation, Work-Energy Theorem and definition of power we obtain the following relationship:

(Eq. 1)

Where:

- Mass of the athlete, measured in kilograms.

- Gravitational constant, measured in meters per square second.

- Climbing rate, measured in meters per second.

- Power, measured in watts.

By the consideration of constant velocity, we get that the climbing rate is represented by:

(Eq. 2)

Where:

- Travelled distance, measured in meters.

- Time, measured in seconds.

And by substituting on (Eq. 1), the following expression is found:

If we know that , , and , then the minimum power output is:

The minimum power output used to accomplish this feat is 408.625 watts.