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Answer :
The rest length of the spaceship is 87.5 meters.
According to the theory of relativity, the length of an object appears to be shorter when it is moving at a relativistic speed. This is described by the Lorentz contraction formula:
L = L₀/γ
where L₀ is the rest length of the object and γ is the Lorentz factor, given by:
γ = 1/√(1 - v²/c²)
where v is the speed of the object and c is the speed of light.
In this case, the spaceship is moving at a speed of 0.900 c relative to the observer, so we can calculate the Lorentz factor as:
γ = 1/√(1 - 0.900²) = 2.294
The observer measures the length of the spaceship to be 38.2 m, which is the length of the spaceship as it appears to them while it is moving at 0.900 c. To find the rest length of the spaceship, we can use the Lorentz contraction formula:
L₀ = L × γ = 38.2 × 2.294 = 87.5 m
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Ther rest length of the spaceship is 87.6 meters.
According to the theory of special relativity, an object's length appears to be shorter when it is moving at high speeds relative to an observer. The length that an object would have when it is at rest (not moving) is called its rest length or proper length.
The relationship between the observed length of an object and its rest length is given by the Lorentz contraction formula
L = L0 / γ
where L is the observed length, L0 is the rest length, and γ (gamma) is the Lorentz factor, which depends on the speed of the object relative to the observer and is given by:
γ = 1 / sqrt(1 - v^2/c^2)
where v is the speed of the object, and c is the speed of light (which is approximately 3.00 x 10^8 m/s).
Substituting the given values, we get:
γ = 1 / sqrt(1 - (0.900c)^2/c^2) = 2.294
L0 = L * γ = 38.2 m * 2.294 = 87.6 m
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