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