Length Contraction: Relative Speed & Time of a Meter Stick?

Question

A meter stick moving with respect to an observer appears only 500 mm long to her. What is its relative speed? How long does it take to pass her? The meter stick is parallel to its direction of motion. what equations do i use

Answer 1

L = L0*SQRT[1 - (v/c)^2]

L = length of ruler as seen by an observer

L0 = the rest length = 1 meter

c = speed of light = 3x10^8 m/s

v = speed of ruler

Actually the ruler will appear to be rotated if we are talking about what the ruler would actually look like.But the degree of rotation will fit the equation.

L = (1/2)L0 = L0*SQRT[1 - (v/c)^2]

(1/4) = 1 - (v/c)^2

(v/c)^2 = (3/4)

v = c*SQRT(3)/2

v = 0.866*c

The ruler would have to be traveling at 0.866 the speed of light.

time = L/v = 0.5m/[0.866*c] = 1.2945x10^(-9) seconds

time = 1.2945 nanoseconds