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27 October, 07:59

A fellow astronaut passes by you in a spacecraft traveling at a high speed. The astronaut tells you that his craft is 21.1 m long and that the identical craft you are sitting in is 17.3 m long. (a) According to your observation, how long is your craft? m (b) According to your observation, how long is the astronaut's craft? m (c) According to your observation, what is the speed of the astronaut's craft relative to your craft?

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  1. 27 October, 10:34
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    A) 21.1 m

    B) 17.3 m

    C) 3.267x10^7 m/s

    Explanation:

    This is a case of special relativity.

    Let the relative speed of astronauts ship to my ship be v.

    According to my observation,

    My craft is 21.1 m long, according to my observation, astronauts craft is 17.3 m long.

    If we fix the reference frame as my ship, then the rest lenght of our identical crafts is 21.1 m and the relativistic lenght is 17.3 m

    l' = 21.1 m

    l = 17.3 m

    From l = l' (1 - p^2) ^0.5

    Where p is c/v, and c is the speed of light

    17.3 = 21.1 x (1 - p^2) ^0.5

    0.82 = (1 - p^2) ^0.5

    Square both sides

    0.67 = 1 - p^2

    P^2 = 0.33

    P = 0.1089

    Revall p = v/c

    v/c = 0.1089

    But c = speed of light = 3x10^8 m/s

    Therefore,

    v = 3x10^8 x 0.1089 = 3.267x10^7 m/s
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