Final answer:
The average power supplied by a 6.00 kg person running up a flight of stairs with a vertical distance of 4.0 m in 4.2 s is approximately 56 watts, calculated using the formula P = work/time, where work is mass times gravity times height.
Step-by-step explanation:
The average power supplied by a person while running up the stairs can be calculated using the work-energy principle. Power is defined as the rate at which work is done or energy is transferred. When the person is running up the stairs, they are doing work against the gravitational force.
The work done (W) by the person can be found by the formula:
W = m × g × h
Where m is the mass of the person, g is the acceleration due to gravity (9.8 m/s2), and h is the vertical distance climbed. So for a 6.00 kg person climbing 4.0 m high stairs:
W = 6.00 kg × 9.8 m/s2 × 4.0 m = 235.2 J
To find the average power (P), we divide the total work done by the time taken (t), which gives us:
P = W / t
P = 235.2 J / 4.2 s ≈ 56 W
Therefore, the average power supplied by the person is approximately 56 watts.