Respuesta :
Answer:
14.625 years
Explanation:
Because acceleration/deceleration are negligent we can simplify this problem into 2 basic parts:
First: how long before the astronaut arrives? Since the speed of the craft is 0.8 times the speed of light and the distance to travel is 6.5 light-years, the equation to answer this part is:
0.8t=6.5
solve for t by dividing by 0.8
t=6.5/0.8 or 8.125
so, she will arrive in 8.125 years.
Then, once she sends her message, it will travel towards earth at 1 times the speed of light or:
1.0t=6.5 which is just t=6.5
so, her message will arrive back to Earth (8.125+6.5) 14.625 years after takeoff.
The time elapsed in earth will be 14.625 years.
To understand this we need to find how much time she took to travel 6.5 light years and then how much time the signal took to reach the earth.
How much time she took to travel 6.5 light year?
0.8t = 6.5 ( because 1 light year = distance travelled by light in a year)
t = 6.5/0.8
t = 8.125 years
So, she travelled for 8.125 year.
How much time it took for the signal?
1.0 t = 6.5 ( because radio signal travells with the same speed of light)
t = 6.5/1.0
t = 6.5 years
- Sum of these two gives us how much time elapsed on earth between two mentioned events.
So, 8.125 + 6.5 = 14.625 years
So, the time elapsed on earth between the launch and the arrivel of the first radio signal is 14.625 years.
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