Time dilation formula,

$\overline{){\mathbf{t}}{\mathbf{=}}\frac{\mathbf{T}}{\sqrt{\mathbf{1}\mathbf{-}{\displaystyle \frac{{v}^{2}}{{c}^{2}}}}}}$

**Part A**

A:

${\mathbf{t}}{\mathbf{=}}\frac{\mathbf{20}}{\sqrt{\mathbf{1}\mathbf{-}{\displaystyle \frac{{(0.4c)}^{2}}{{c}^{2}}}}}$

t_{A} = 21.82 years

B:

${\mathbf{t}}{\mathbf{=}}\frac{\mathbf{5}}{\sqrt{\mathbf{1}\mathbf{-}{\displaystyle \frac{{(0.2c)}^{2}}{{c}^{2}}}}}$

t_{B} = 5.10 years

C:

${\mathbf{t}}{\mathbf{=}}\frac{\mathbf{10}}{\sqrt{\mathbf{1}\mathbf{-}{\displaystyle \frac{{(0.8c)}^{2}}{{c}^{2}}}}}$

Time Dilation Ranking Task

Five identical quintuplets leave earth when they reach the age of 21, in the year 2121. Each quintuplet goes on a spaceship journey that takes T years, as measured by a clock in each spaceship. During the journey, they travel at a constant speed v, as measured on earth, except during the relatively short acceleration phases of their journey.**Part A. **Rank these quintuplets on the basis of the year on earth when they return from their journey. Rank from largest to smallest. To rank items as equivalent, overlap them.

A: T=20 years, v=0.4c

B: T= 5 years, v=0.2c

C: T=10 years, v=0.8c

D: T=10 years, v=0.4c

E: T=20 years, v=0.8c

**Part B.** Rank these quintuplets on the basis of their age when they return from their journey. Rank from largest to smallest. To rank items as equivalent, overlap them.

A: T=20 years, v=0.4c

B: T= 5 years, v=0.2c

C: T=10 years, v=0.8c

D: T=10 years, v=0.4c

E: T=20 years, v=0.8c

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Consequences of Relativity concept. You can view video lessons to learn Consequences of Relativity. Or if you need more Consequences of Relativity practice, you can also practice Consequences of Relativity practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Jerousek's class at UCF.