Question

In 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

42.11 years old

Step-by-step explanation:

Given that:

In 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

To find her age we use:

`\Delta t_m=\frac{\Delta t_s}{\sqrt{1-(v^2)/(c^2) } }\\`

Δtm is time interval for the observer stationary relative to the sequence of

events = 2040 - 2000 = 40 years

Δts is is the time interval for an observer moving with a speed v relative to the sequence of event

v = velocity = 2.5 x 10^8 m/s

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

`\Delta t_s=\Delta t_m}{\sqrt{1-(v^2)/(c^2) } }\\\Delta t_s=40\sqrt{1-((2.5*10^8)^2)/((3*10^8)^2)}\\\Delta t_s=22.11\ yr`

Here age in 2000 is 20 year, therefore when she appear she would be 20 year + 22.11 year = 42.11 years old