Answer:
8 signals received by twin A during the trip.
Explanation:
Given that,
Distance = 12 light year
Speed = 0.6 c
Time = 1 year
We need to calculate the time by A
Using formula of time
[tex]T=t\sqrt{\dfrac{1+\dfrac{v}{c}}{1-\dfrac{v}{c}}}[/tex]
Put the value into the formula
[tex]T=1\sqrt{\dfrac{1+0.6}{1-0.6}}[/tex]
[tex]T=2\ years[/tex]
Similarly,
The expression for distance cover by A
[tex]D=d\sqrt{1-\dfrac{v^2}{c^2}}[/tex]
[tex]D=12\sqrt{1-(0.6)^2}[/tex]
[tex]D=9.6\ ly[/tex]
We need to calculate the time
Using formula of time
[tex]t=\dfrac{D}{v}[/tex]
[tex]t=\dfrac{9.6}{0.6}[/tex]
[tex]t=16\ years[/tex]
We need to calculate the signals received by twin A
Using formula for number of signals
[tex]n=\dfrac{t}{T}[/tex]
Put the value into the formula
[tex]n=\dfrac{16}{2}[/tex]
[tex]n=8\ signals[/tex]
Hence, 8 signals received by twin A during the trip.
