Both do the same work, but the faster individual expends more power.
Explanation
In physics, Work is defined as the energy transferred to or from an object via the application of force along a displacement. Power is the rate at which work is done or energy is transferred over time.
Detailed Analysis:
- Work Done: When an individual climbs to a certain height, they perform work against the force of gravity. The work done ($W$) is calculated as the product of the individual's weight ($mg$) and the vertical height ($h$) climbed:
$$W = mgh$$
Since both individuals have equal weight and climb to the same height, the work done by both is identical. - Power Expended: Power ($P$) is defined as work done per unit time:
$$P = \frac{W}{t}$$
Since the work done ($W$) is the same for both individuals, power is inversely proportional to the time taken ($t$). Therefore, the individual who takes less time (the faster individual) has a larger denominator in the time variable, resulting in a higher power output.
Conclusion:
Both individuals perform the exact same amount of work, but the one who climbs faster generates more power.
Key Takeaway:
Work is path-independent and time-independent in a conservative field like gravity, depending only on vertical displacement and weight. Power, however, is time-dependent; doing the same work in less time requires greater power.