Question

If an astronaut could travel a v 0.980c for at time oft 12.0 hr as measured on Earth, how much time would the astronauts measure for the trip? What would the distance traveled be according to an observer on Earth? What would the distance traveled be according to the astronaut?

Answer 1

Time observed by the astronaut = 2.388 hours

Distance traveled be according to an observer on Earth = 1.27 × 10¹¹ m

Distance traveled according to the astronaut = 2.52 × 10¹² m

Step-by-step explanation:

Given:

Speed of the astronaut, v = 0.980c

time = 12.0 hr

now, from the time dilation formula we have

`t'=t*\sqrt{1-(v^2)/(c^2)}`

here

t' is the time observed by the astronaut

c is the speed of the light = 3 × 10⁸ m/s

thus,

`t'=12*\sqrt{1-((0.980c)^2)/(c^2)}`

or

t' = 2.388 hours

Now,

Distance = Velocity × time

The distance traveled be according to an observer on Earth will be

Distance = 0.980c × ( 12 × 60 × 60 )

or

D = 0.980 × 3 × 10⁸ × ( 12 × 60 × 60 )

or

Distance = 1.27 × 10¹¹ m

And, The distance traveled according to the astronaut will be

Distance = velocity × t'

or

D = 0.980 × 3 × 10⁸ × ( 2.388 × 60 × 60 )

or

Distance = 2.52 × 10¹² m