Saturday, January 22, 2011

Mastering Physics: How Tall Really Is Your Favorite Superhero?

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 50.0 \% 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 1.82 m. If the superhero landed next to you, how tall would she be when standing?

When standing next to you, the superhero is at rest relative to you, so her height is a proper length. When she is flying, she will look shorter because of length contraction.
Part B
What is the height of the 102nd floor of the Empire State Building as measured by the superhero while flying above it?

Since the superhero is flying parallel to the ground, when she estimates the height of the building, she is measuring a distance in a direction perpendicular to the relative motion. Therefore, she will not observe any length contraction.

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