Question

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

Answer:

You are at the top of the Empire State Building on the 102nd floor, which is located 373 m above the ground when your favorite superhero flies over the building parallel to the ground at 70.0% the speed of light.

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?

Step-by-step explanation:

so this problem is from Einstein's special theory of relativity about length contraction.

the formula is given by:

$L'=L\sqrt{1-\beta^2 }$

where $\beta =v/c$

c is speed of light $c=3*10^8 m/s$ and v is velocity of object.

L is called proper length. L' is length that the observer measure in moving frame.

here velocity of object is 70% speed of light. i.e   $v=209 854 721 m / s$

so $L=1.57 m$

putting all values

$L'= 1.57m \sqrt{1-(\frac{209854721}{3*10^8})^2 } \\\\L'=1.12m$