Final answer:
The work done by a 65.0 kg person climbing stairs and gaining a height of 2.60 meters is calculated using the formula for gravitational potential energy, resulting in approximately 1657.89 J.
Step-by-step explanation:
To find the work done by a 65.0 kg person climbing stairs and gaining 2.60 meters in height, we can use the formula for gravitational potential energy (GPE), which is the work done against gravity to lift an object to a certain height. The formula is GPE = mgh, where m is the mass of the person, g is the acceleration due to gravity (9.81 m/s2), and h is the height gained.
The work done by the person can be calculated as:
Work done = mgh
Work done = (65.0 kg)(9.81 m/s2)(2.60 m)
Work done = (65.0 kg)(25.506 m2/s2)
Work done = 1657.89 Joules (J)
Therefore, the work done by the person is approximately 1657.89 J.