(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The starships of the Solar Federation are marked with the symbol of the Federation, a circle, whereas starships of the Denebian Empire are marked with the Empire's symbol, an ellipse whose major axis is n times its minor axis (a=nb in the figure ).

2. Relevant equations

L=(1-(v/c)^2)l

3. The attempt at a solution

x = rest length of major axis = nb

L = observed length of major axis when ship is travelling at speed v and must be equal to b since you want the ellipse to look like federation circle

b = nb[SQRT(1 - v^2/c^2)] then

to this (1/n)^2 = 1 - v^2/c^2

solve for V....v^2 = (c^2)[1 - (1/n)^2] = (c^2)[ (n^2 - 1)/n^2]

then arrive at v = (c/n)*SQRT[(n^2 - 1)].

i also did this.

L=(1-(v/c)^2)l

b=nb[SQRT(1 - (v/c)^2)]

then i got ((1/n)^2)^1/2)= 1-v/c ---> 1-1/n=v/c

solving for v i got v= c(1-c/n)

i'm not sure which one is correct and don't under stand y different answer.

#1v = (c/n)*SQRT[(n^2 - 1)].

#2 v= c(1-c/n)

im lost

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# Homework Help: The Empire Strikes Back length contraction.

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