Calculate the length of a 120m (as measured by the astronaut) spaceship travelling at 0.85c as measured by a stationary observer

The length of the spaceship of 120m was measured at rest relative to the spaceship so we will take that as the proper length, dennoted Lproper

We first calculate the Lorentz factor:

Ɣ = 1/sqrt(1-(v/c)2)

Ɣ = 1/sqrt(1-0.852)

Ɣ = 1.8986...  (Keep this number in your calculator as rounding now will affect your final answer)

Now, relate this to the formula for length contraction:

L = Lproper / Ɣ

L = 120/1.8986...

L = 63.2m as measured by the stationary observer

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