A \( 60-\mathrm{kg} \) woman runs up a flight of stairs having a rise of 4.0 m in a time of 4.2 s . What average power did she supply? 1) 380 W 2) 560 W 3) 620 W 4) 670 W 5) 730 W

To find the average power supplied by the woman, we can use the formula for power, which is the work done divided by the time taken. The work done against gravity when ascending is given by: \[ \text{Work} = m \cdot g \cdot h \] where: - \( m = 60 \, \mathrm{kg} \) (mass of the woman), - \( g = 9.81 \, \mathrm{m/s^2} \) (acceleration due to gravity), - \( h = 4.0 \, \mathrm{m} \) (height of the stairs). Calculating the work done: \[ \text{Work} = 60 \, \mathrm{kg} \cdot 9.81 \, \mathrm{m/s^2} \cdot 4.0 \, \mathrm{m} = 2354.4 \, \mathrm{J} \] Now, with the time taken being \( t = 4.2 \, \mathrm{s} \), we can calculate the average power: \[ \text{Power} = \frac{\text{Work}}{t} = \frac{2354.4 \, \mathrm{J}}{4.2 \, \mathrm{s}} \approx 560.1 \, \mathrm{W} \] The closest answer here is \( 560 \, \mathrm{W} \). So the answer is: 2) 560 W