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?

Answer 1

she'll be 42.3 years old

Step-by-step 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 - (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