A cyclist is coasting at 13 m/s when she starts down a 460 m long slope that is 30 m high. The cyclist and her bicycle have a combined mass of 70 kg. A steady 15 N drag force due to air resistance acts on her as she coasts all the way to the bottom. What is her speed at the bottom of the slope?

The value is  

Explanation:

From the question we are told that

   The velocity is

    The  length of the slope is

    The height of the slope is

     The mass of the cyclist and her bicycle is

   The drag force is  

Generally from the law of energy conservation we have that

Here is the potential energy at the top of the slope which is mathematically represented as

=>      

=>    

and   is the kinetic energy at the top of the slope which is mathematically represented as

=>    

=>    

And  W is the work done by the bicycle which is mathematically represented as

=>    

=>    

and is the kinetic energy at the bottom of the slope which is mathematically represented as

=>    

=>    

So

=>    

explanation:

newton's third law, for every action there is an equal and opposite reaction.