Question

You are at the top of the Empire State Building on the 102nd floor, which is located 373 mm above the ground, when your favorite superhero flies over the building parallel to the ground at 70.0 %% the speed of light. Part A You have never seen your favorite superhero in real life. Out of curiosity you calculate her height to be 1.57 mm . If the superhero landed next to you, how tall would she be when standing

Answer 1

L₀ = 0.0022 m = 2.2 mm

Step-by-step explanation:

Here, we will use the length contraction formula from the theory of relativity presented by Einstein:

`L = L_o\sqrt{1-(v^2)/(c^2)}`

where,

L = Relative length = 1.57 mm = 0.00157 m

L₀ = actual length at rest = ?

c = speed of light

v = relative speed = 70% of c = 0.7 c

Therefore,

`0.00157\ m = L_o\sqrt{1-((0.7\ c)^2)/(c^2) }\\\\L_o = (0.00157\ m)/(√(1-0.49))`

L₀ = 0.0022 m = 2.2 mm