A rocket ship flies past the earth at 82.0 of the speed of light. Inside, an ast

Question

A rocket ship flies past the earth at 82.0 of the speed of light. Inside, an astronaut who is undergoing a physical examination is having his height measured while he is lying down parallel to the direction the rocket ship is moving. If his height is measured to be 1.96 by his doctor inside the ship, what height would a person watching this from earth measure for his height? If the earth-based person had measured 1.96 , what would the doctor in the spaceship have measured for the astronaut's height?

Explanation / Answer

Given speed of rocket ship v = 82 % of speed of light                                     = 0.82 c Proper length of the astronaut L p = 1.96 m According to length contraction The length of astronaut with respect a person watching from earth is                              L = L p 1 - v 2 /c 2                                  = ( 1.96 m ) 1 - 0.822                                  = 1.121 m ______________________________________________________ If the earth based person has measured 1.96 m length of astronaut with respect to the doctor in the spaceship is                            L p = L / 1 - 0.822                                   = 1.96 / 0.5723                                   = 3.424 m

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