Sarah and her bicycle have a total mass of 40 kg. Her speed at the top of a 10 m high and 100m long hill is 5 m/s. If the force of friction on her way down is 20 N, at what speed will she be going when she reaches the bottom

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:

  (1)

There is no energy conservation because there is a force of friction on her way down.  

By entering , where 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:

In the initial state, we have kinetic and potential energy and in the final state, we have only kinetic energy.

Where:

m: is the total mass = 40 kg

: is the final speed =?

: is the intial speed = 5 m/s

g: is the gravity = 9.81 m/s²

h: is the height = 10 m

By solving the above equation for we have:

Therefore, she will be going at 11.01 m/s when she reaches the bottom.                                    

I hope it helps you!