Question

the length of the rod is found to be half of it's length when at rest what is the speed of the rod relative to the observer?​

Answer 1

L is the length observed by an observer in motion relative to the object.

L0 is the proper length.

v is the relative velocity between the observer and the moving object.

c is the speed of light.

By solving this equation for L=L0/2

sqrt(1−(v/c)2))=1/2

1−(v/c)2=1/4

(v/c)2=3/4

v2=(3/4)∗c2

v=(sqrt(3))/2∗c

v=0.866c

Thus, at about 86.6% the speed of light or 259 627 884 m/s , length of the moving object will have contracted to half its proper length.

Please note: both L and L0 are measured parallel to the object's line of movement.

EDIT: Added more explanation to the equation from Wiki in case someone don’t know what the symbols stand for.

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