Two observers, one stationary and one moving at a constant velocity of 0.8c (80% of the speed of light), measure the length of a spaceship. Calculate the spaceship's contracted length as observed by the moving observer.
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To calculate the spaceship's contracted length as observed by the moving observer, we can use the Lorentz contraction formula:
L' = L * sqrt(1 - (v^2 / c^2))
Where L' is the contracted length, L is the rest length (as measured by the stationary observer), v is the velocity of the moving observer, and c is the speed of light.
Given that the moving observer is moving at a velocity of 0.8c (80% of the speed of light), we can substitute the values into the formula:
L' = L * sqrt(1 - (0.8c^2 / c^2))
= L * sqrt(1 - 0.64)
= L * sqrt(0.36)
= L * 0.6
Therefore, the spaceship's contracted length as observed by the moving observer is 0.6 times the rest length (as measured by the stationary observer).
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