Question

N 2000, a 20-year-old astronaut left Earth to explore the galaxy; her spaceship travels at 2.5 x 10^8 m/s. She returns in 2040. About how old will she appear to be?

Answers

  1. Answer:

    she’ll be 42.3 years old

    Explanation:

    The year she left is 2020

    she returns in 2040

    the time observed to have passed by on earth is 40 years

    she traveled at a speed of 2.5 x 10^8 m/s

    From relativity, the astronaut will experience a time dilation and will age more slowly.

    the time that is observed to pass on her ship will be gotten from

    t’ = t\sqrt{1 - \frac{v^{2} }{c^{2} } } }

    where t is the time that is observed to pass by an earthly observer

    v is the speed of her ship

    c is the speed of light = 3 x 10^8 m/s

    v/c = 2.5/3 = 0.83  

    t’ = 40{\sqrt{1 - 0.83^{2} } } = 40 x 0.5578 = 22.3 years would have passed for her

    This means that she’ll be 20 + 22.3 = 42.3 years old

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