The length of the spaceship as measured by an earth-bound observer is equal to 48.6 m
Length contraction can be described as the phenomenon that the length is measured to be shorter than its proper length, which is the length as measured in its own rest frame and is also known as Lorentz contraction.
The original formula of the length contraction leads to the relation:
[tex]{\displaystyle L=L_{0}{\sqrt {1-\frac{v^{2}}{c^{2}}}}[/tex]
In the above equation, both L and L₀ are measured parallel to the line of movement of the object.
Given, the original length of the spaceship, L₀ = 200 m
The speed of the spaceship, v = 0.970 c
The apparent length of the spaceship can be calculated as:
[tex]{\displaystyle L=200\times {\sqrt {1-\frac{(0.970c)^{2}}{c^{2}}}}[/tex]
L = 48.6 m
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Your question was incomplete, most probably the complete question was,
A spaceship, 200 m long as seen on board, moves by the earth at 0.970c. What is its length as measured by an earth-bound observer?
