To calculate the power used by the woman, we can use the formula for power, which is:
\[ \text{Power} = \frac{\text{Work}}{\text{Time}} \]
First, we need to calculate the work done against gravity when she climbs the stairs. The work done (W) can be computed using the formula:
\[ W = m \cdot g \cdot h \]
where:
- \(m\) is the mass (48 kg),
- \(g\) is the acceleration due to gravity (approximately \(9.81 , \text{m/s}^2\)),
- \(h\) is the height (12 m).
Now, we can calculate the work done:
\[ W = 48 , \text{kg} \cdot 9.81 , \text{m/s}^2 \cdot 12 , \text{m} \]
Calculating this step-by-step:
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Calculate \(48 \cdot 9.81\):
\[ 48 \cdot 9.81 \approx 470.88 , \text{N} \]
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Now multiply by 12 m:
\[ W \approx 470.88 , \text{N} \cdot 12 , \text{m} \approx 5666.56 , \text{J} \]
Next, we calculate the power by dividing the work done by the time taken (30 s):
\[ \text{Power} = \frac{5666.56 , \text{J}}{30 , \text{s}} \approx 188.85 , \text{W} \]
Thus, the power used by the woman while climbing the stairs is approximately 188.85 watts.
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