Given,
The mass of the girl, m=58 kg
The height of the staircase, h=52 m
The time she takes to run up the staircase, t=23 s
The work the girl does to climb up the staircase is equal to the change in the potential energy of the girl.
Thus the work done is given by,
[tex]W=\text{mgh}[/tex]Where g is the acceleration due to gravity.
On substituting the known values,
[tex]\begin{gathered} W=58\times9.8\times52 \\ =29.56\times10^3\text{ J} \end{gathered}[/tex]The power output is equal to the rate at which the work is done
Thus the power output is given by,
[tex]P=\frac{W}{t}[/tex]On substituting the known values,
[tex]\begin{gathered} P=\frac{29.56\times10^3}{23} \\ =1285.22\text{ W} \end{gathered}[/tex]Thus the maximum power output is 1285.22 W
