Answer:
<em>0.97c</em>
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Explanation:
From the relativistic equation for length contraction, we have
=
where
is the final length of the object
is the original length of the object before contraction
β =
where v is the speed of the object
c is the speed of light in free space = 3 x 10^8 m/s
The equation can be re-written as
/
=
For the length to contract to one-fourth of the proper length, then
/
= 1/4
substituting into the equation, we'll have
1/4 =
substituting for β, we'll have
1/4 =
squaring both side of the equation, we'll have
1/16 = 1 -
= 1 - 1/16
= 15/16
square root both sides of the equation, we have
v/c = 0.968
v = <em>0.97c</em>
