- #1
seto6
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Homework Statement
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 ).
Homework Equations
L=(1-(v/c)^2)l
The Attempt at a Solution
x = rest length of major axis = nb
L = observed length of major axis when ship is traveling 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