# Problem: Time Dilation Ranking TaskFive 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=0.4cB: T= 5 years, v=0.2cC: T=10 years, v=0.8cD: T=10 years, v=0.4cE: T=20 years, v=0.8cPart 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=0.4cB: T= 5 years, v=0.2cC: T=10 years, v=0.8cD: T=10 years, v=0.4cE: T=20 years, v=0.8c

###### FREE Expert Solution

Time dilation formula,

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

Part A

A:

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

tA = 21.82 years

B:

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

tB = 5.10 years

C:

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

###### Problem Details

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