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: \[ \text{Power} = \frac{\text{Work Done}}{\text{Time Taken}} \] Given: - Mass of the woman (\( m \)) = 60 kg - Rise of the stairs (\( h \)) = 4.0 m - Time taken (\( t \)) = 4.2 s First, we need to calculate the work done by the woman in lifting herself up the stairs. The work done is given by the formula: \[ \text{Work Done} = m \times g \times h \] where \( g \) is the acceleration due to gravity, approximately 9.8 m/s^2. Now, we can calculate the work done and then find the average power supplied by the woman. Calculate the value by following steps: - step0: Calculate: \(60\times 9.8\times 4\) - step1: Multiply the terms: \(588\times 4\) - step2: Multiply the numbers: \(2352\) Calculate or simplify the expression \( 2352/4.2 \). Calculate the value by following steps: - step0: Calculate: \(\frac{2352}{4.2}\) - step1: Convert the expressions: \(\frac{2352}{\frac{21}{5}}\) - step2: Multiply by the reciprocal: \(2352\times \frac{5}{21}\) - step3: Reduce the numbers: \(112\times 5\) - step4: Multiply the numbers: \(560\) The average power supplied by the woman is 560 W. Therefore, the correct answer is option 2) 560 W.