A spaceship passes you at 0.95c. You note its length to be 80.0 m. How long is it when at rest?

Answer 1

Answer: 256m

Method:

1. Lorentz equation for length contraction is L'= L / γ, which means the proper length (length of spaceship in rest frame) (L) divided by the Lorentz Factor (γ is the letter gamma but it looks like garbo using wyzants greek letters) is equal to the Length as measured by an observer ( L' ).
2. Lorentz Factor γ = 1/(√(1-(v/c)^2))
3. In the problem, L' = 80.0m , v = 0.95c, and we need to find rest length (L)

Calculation

1. γ = 1/(√(1-(.95)^2)) = 3.203
2. L = L' • γ = 3.203 • 80m = 256 m