Can Anna Reach Planet 2 in 30 Years?

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SUMMARY

In the discussion, participants analyze the problem of whether Anna can reach Planet 2 in 30 years, given that light takes 40 years to travel the same distance. The key equations involved are L=Lo/Yv, V=Dist/Time, and Yv=1/(1-V^2/c^2)^(1/2). The conclusion is that if Anna travels at 0.8c, she can indeed reach Planet 2 in the specified time. The confusion arises from the manipulation of the equations, particularly the division by c, which is essential for correctly applying the principles of relativistic physics.

PREREQUISITES
  • Understanding of special relativity concepts, particularly time dilation and length contraction.
  • Familiarity with the equations of motion in relativistic physics.
  • Knowledge of the speed of light as a constant (c) and its implications in physics.
  • Basic algebra skills for manipulating equations and solving for variables.
NEXT STEPS
  • Study the implications of time dilation in special relativity using examples.
  • Learn how to derive and apply the Lorentz factor (Yv) in various scenarios.
  • Explore the concept of relativistic velocity addition and its applications.
  • Review problems involving distances measured in light-years and their conversions in relativistic contexts.
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This discussion is beneficial for physics students, educators, and anyone interested in understanding the principles of special relativity and their applications in theoretical scenarios involving high-speed travel.

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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.
 
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thharrimw said:
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?
 
Nonclasical Physics by Randy Harris
 

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