Conservation of energy / work problem

[adams_695]

Homework Statement

Call the system the bicycle and the rider. Use the work-energy equation and W = Fd. Assume the cyclist and air do not heat up. The work-energy equation is Kf + Ugf = Ki + Ugi + W.

Relevant Equations

Kinetic energy & gravitational energy

If someone could advise what I've done wrong it would be much appreciated. How have they eliminated the initial and final for y, and simplify only to y? Also, how did they simplify to a positive 2? What algebraic steps have I missed? Thanks for your help.

 

[haruspex]

I would not call that a problem statement. What is the actual question?

 

[adams_695]

I would not call that a problem statement. What is the actual question?

Sorry here it is. Question 9. Thanks!

 

[haruspex]

You are told the top of the hill is 30m higher than the bottom of the hill. So what is y_i-y_f?

 

[adams_695]

You are told the top of the hill is 30m higher than the bottom of the hill. So what is y_i-y_f?

30m-0m.

Is this how I went wrong when solving algebraically in the image of my working?

 

[Chandra Prayaga]

There was nothing wrong in what you worked out. As haruspex pointed out, identify yi and yf in your own algebra and you are done.

 

[haruspex]

30m-0m.

Is this how I went wrong when solving algebraically in the image of my working?

The last line of your working has the terms -2gy_f+2gy_i. Factorise.