Answer:
Approximately [tex]127.5\; {\rm W}[/tex] on average.
Explanation:
Power is the rate at which work is being done. To find average power, divide the total amount of work done by the duration of the motion. While it is given that the duration of the motion in this question is [tex]t = 60.0\; {\rm s}[/tex], the amount of work done needs to be found.
The girl is acting against the downward gravitational pull of [tex]510\; {\rm N}[/tex]. The force she exerts would be equal in magnitude and opposite in direction: [tex]510\; {\rm N}\![/tex] upward.
The work that is done is equal to the product of the force and the displacement the direction of the force. Given that the girl is [tex]15.0\; {\rm m}[/tex] above the initial position, that displacement would be [tex]15.0\; {\rm m}\![/tex]. The work done in this process would be:
[tex](510\; {\rm N})\, (15.0\; {\rm m}) = 750\; {\rm J}[/tex].
To find the average power, divide the amount of work done by the duration of the motion:
[tex]\begin{aligned} & (\text{average power}) \\ =\; & \frac{(\text{total work})}{(\text{duration})} \\ =\; & \frac{765\; {\rm J}}{60.0\; {\rm s}} \\ =\; & 127.5\; {\rm W}\end{aligned}[/tex].
In other words, the average power exerted during this motion is [tex]127.5\; {\rm W}[/tex].
