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Length Contraction spaceship Problem

  • Thread starter hbrinn
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  • #1
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Homework Statement


A spaceship passes you at a speed of .750c. You measure its length to be 28.2 m. How long would it be when at rest?


Homework Equations


I think the equation that is relevant is L=L(sub0)xsqrt(1-v^2/c^2)


The Attempt at a Solution


L=28.2xsqrt(1-(.75^2))=18.65m
Apparently, the answer is 42.6 m. I can't even imagine how to get 42.6 from that.
 

Answers and Replies

  • #2
collinsmark
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Homework Statement


A spaceship passes you at a speed of .750c. You measure its length to be 28.2 m. How long would it be when at rest?


Homework Equations


I think the equation that is relevant is L=L(sub0)xsqrt(1-v^2/c^2)


The Attempt at a Solution


L=28.2xsqrt(1-(.75^2))=18.65m
Apparently, the answer is 42.6 m. I can't even imagine how to get 42.6 from that.
I think you just got your variables swapped. If you are using

[tex] L = L_0 {\sqrt{1 - \frac{v^2}{c^2}} [/tex]

then [tex] L [/tex] is 28.2 m, and you need to solve for [tex] L_0 [/tex], the length when the relative velocity is 0. [tex] L [/tex] is the length when traveling at speed [tex] v [/tex].
 
  • #3
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Then by that logic isn't the answer 64.457?

I did 28.2=L(1-.75^2). Is that wrong?
 
  • #4
collinsmark
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Then by that logic isn't the answer 64.457?

I did 28.2=L(1-.75^2). Is that wrong?
You forgot to take the square root. :tongue2:
 
  • #5
vela
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You forgot the square root.
 
  • #6
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Yay! Thank you very much!
 

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