Forming Proper Equation to Calculate Speed of Spaceship

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SUMMARY

The discussion focuses on calculating the speed of a spaceship required for its observed length to be half of its proper length. Given a proper length (Lo) of 67 meters and an observed length (L) of 33.5 meters, the equation used is L = (Lo)(sqrt(1-(v^2)/(c^2))). The correct calculation for speed (v) is derived as v = sqrt((1-(L/Lo)^2)(c^2)). The error identified was in the arithmetic, specifically the division of Lo by L, which led to confusion in the calculations.

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"proper" Length

What speed would the spaceship have to travel for its relative length to be half its “proper” length

Given:
Lo = 67m
L = 33.5

Required:
v

Analysis:
L = (Lo)(sqr(1-(v^2)/(c^2)))

Now, I calculate v = sqr((1-(L/Lo)^2)(c^2)) however that gives me an non-real anwer. Clearly my algebra is lacking somewhere.

Can anyone help me form a proper equation for this?
 
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Your algebra looks fine. Your arithmetic seems to be lacking. L/Lo=1/2, 1-(1/2)^2=3/4 etc etc.
 
Ah, yes, I was dividing Lo/L on paper. It is always the simplest things...

Thanks
 

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