Calculate the length contraction experienced by a spaceship traveling at 0.95 times the speed of light as observed from Earth, assuming the spaceship is 100 meters in length when at rest.
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The formula for calculating length contraction is given by:
Length_contraction = Rest_length * sqrt(1 - (v^2/c^2))
Where:
Rest_length = 100 meters (given)
v = 0.95c (speed of spaceship)
c = speed of light = 3 x 10^8 meters/second
Substituting the given values into the formula:
Length_contraction = 100 * sqrt(1 - (0.95^2 / 1^2))
Length_contraction = 100 * sqrt(1 - 0.9025)
Length_contraction = 100 * sqrt(0.0975)
Length_contraction ≈ 100 * 0.312
Length_contraction ≈ 31.2 meters
Therefore, the length of the spaceship will be contracted to approximately 31.2 meters as observed from Earth while it is traveling at 0.95 times the speed of light.
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