Question

A starship travels to a planet that is 20 light years away. The astronauts stay on the planet for 2.0 years before returning at the same speed and they are greeted back on earth 52 years after they left. Assume that the time needed to accelerate and decelerate is negligible. How much have the astronauts aged? (a) 15 years, (b) 20 years, (c) 22 years, (d) 30 years, (e) 32 years.

Answer 1

Answer:

astronauts age is 32 years

correct option is e 32 years

Explanation:

given data

travels = 20 light year

stay = 2 year

return = 52 years

to find out

astronauts aged

solution

we know here they stay 2 year so time taken in traveling is

time in traveling = ( 52 -2 )  = 50 year

so it mean 25 year in going and 25 years in return

and distance is given 20 light year

so speed will be

speed = distance / time

speed = 20 / 25 = 0.8 light year

so time is

time = $\frac{t}{\sqrt{1-v^2} }$

time =  $\frac{25}{\sqrt{1-0.8^2} }$

time = 15 year

so age is 15 + 2 + 15

so astronauts age is 32 years

so correct option is e 32 years