The time elapsed is 3.23 years.
To find the time elapsed, we will begin with calculation of distance traveled. Subsequently we will calculate time elapsed.
The formula to be used for finding out the distance traveled is -
[tex]x_{0} =[/tex] [tex]x\sqrt{1-\frac{v^{2}}{c^{2} } }[/tex]
In this formula, x₀ represents distance traveled, x represents distance measured at Earth, v is spaceship velocity and c is speed of light. Now, keeping the values in formula to find the value of distance traveled.
[tex]x_{0} =4.3\sqrt{1-\frac{(0.8c)^{2} }{c} }[/tex]
[tex]x_{0} =4.3\sqrt{0.36 }[/tex]
[tex]x_{0} = 2.58[/tex] light years
Now, we know the distance traveled. Also, distance and time are related to each other by the formula -
[tex]Speed = \frac{distance}{time}[/tex]
Speed of spaceship = 0.8c
Distance traveled = 2.58 light years
Again keep the values in formula to find the time elapsed.
Time = [tex]\frac{2.58}{0.8c}[/tex]
Time = 3.23 years
Hence, 3.23 years would elapse on a clock on board the spaceship.
Practice more problems on light years -
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