A meter moving with respect to an observer appears only 500mm long to her. what is its relative speed?. how long does it take to pass her?. the meter stick is paralllel to its direction of motion.
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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
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