You take a trip to a star located 1,000 light-years away and return.You travel at an average speed of 0.99c.
HINT: The time dilation formula is:
$ t^{\prime}=\sqrt[t]{1-\left(\frac{v}{c}\right)^{2}} $
-About how many years will pass on Earth while you are gone?

Question

You take a trip to a star located 1,000 light-years away and return.You travel at an average speed of 0.99c.
HINT: The time dilation formula is: 
$ t^{\prime}=\sqrt[t]{1-\left(\frac{v}{c}\right)^{2}} $
-About how many years will pass on Earth while you are gone?

Quizplus · Accepted Answer

The time dilation formula is given as $ t' = t \sqrt{1-\left(\frac{v}{c}\right)^2} $, but to find the time experienced on Earth, we need to consider the total distance traveled (2,000 light-years, there and back) and the speed (0.99c). The formula provided seems to be incorrectly stated for this context. The correct approach involves calculating the time it takes from Earth's frame of reference, which is simply distance/speed. Since the traveler moves at 0.99c, and the round trip covers 2,000 light-years, the time on Earth would be $ \frac{2000 \, \text{light-years}}{0.99c} \approx 2020 \, \text{years} $. However, due to the choices provided and rounding, 2,000 years is the closest and correct choice, indicating a misunderstanding in the hint provided.

You Take a Trip to a Star Located 1,000 Light-Years t′=1−(vc)2t t^{\prime}=\sqrt[t]{1-\left(\frac{v}{c}\right)^{2}} t′=t1−(cv​)2​

You Take a Trip to a Star Located 1,000 Light-Years $t^{\prime}=\sqrt[t]{1-\left(\frac{v}{c}\right)^{2}}$