Answer:
She will be going at 11.01 m/s when she reaches the bottom.
Explanation:
We can find the speed at the bottom by equating the total work with the change in energy:
[tex] W = E_{f} - E_{i} [/tex] (1)
There is no energy conservation because there is a force of friction on her way down.
By entering [tex]W = -F_{\mu}*d[/tex], where [tex]F_{\mu}[/tex] is the force of friction (is negative because it is in the opposite direction of motion) and d is the displacement, into equation (1) we have:
[tex]-F_{\mu}*d = E_{f} - E_{i}[/tex]
In the initial state, we have kinetic and potential energy and in the final state, we have only kinetic energy.
[tex]-F_{\mu}*d = \frac{1}{2}mv_{f}^{2} - (\frac{1}{2}mv_{i}^{2} + mgh)[/tex]
Where:
m: is the total mass = 40 kg
[tex]v_{f}[/tex]: is the final speed =?
[tex]v_{i}[/tex]: is the intial speed = 5 m/s
g: is the gravity = 9.81 m/s²
h: is the height = 10 m
[tex] -20 N*100 m = \frac{1}{2}40 kg*v_{f}^{2} - \frac{1}{2}*40 kg*(5 m/s)^{2} - 40 kg*9.81 m/s^{2}*10 m [/tex]
By solving the above equation for [tex]v_{f}[/tex] we have:
[tex] v_{f} = 11.01 m/s [/tex]
Therefore, she will be going at 11.01 m/s when she reaches the bottom.
I hope it helps you!
