Can Anna Reach Planet 2 in 30 Years?

[thharrimw]

Homework Statement

It takes light 40 years to get from planet 1 to planet 2 anna who was just born leves planet 1 to go to planet 2. can she make it to planet 2 in 30 years?

Homework Equations

L=Lo/Yv
V=Dist/Time
Yv=1/(1-V^2/c^2)^(1/2)

The Attempt at a Solution

I know the anwser is yesand if anna moves at .8c she would make it in 30 years but i need help understanding why.
in my book it says to take V=40LY/30Y and i get that part but then it says to divide both sides by c and it gets V/C=(40LY/30Y)((1-V^2/c^2)^(1/2))
i want to know WHY you have to divide one side by c tha the other side by 1/(c(1-V^2/c^2)^(1/2))
after that step i understand it but that step is confusing me.

 

[Doc Al]

in my book it says to take V=40LY/30Y

I don't quite understand that. Instead I'd take V = Dist/Time = (Lo/γ)/T = (40LY/γ)/30Y. Then it's just a matter of solving for V.

and i get that part but then it says to divide both sides by c and it gets V/C=(40LY/30Y)((1-V^2/c^2)^(1/2))
i want to know WHY you have to divide one side by c tha the other side by 1/(c(1-V^2/c^2)^(1/2))

That's incorrect. You'd divide both sides by c. But you must start with the correct equation.

What book are you using?

 

[thharrimw]

Nonclasical Physics by Randy Harris