Which Quintuplet Returns to Earth Last Based on Time Dilation Ranking?

[kolua]

Homework Statement

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.

Rank these quintuplets on the basis of their age when they return from their journey.
Rank from largest to the smallest.

Homework Equations

A .T= 20yr, v=0.4c
B. T= 10yr, v=0.4c
C. T= 20yr, v=0.8c
D. T= 5yr, v=0.8c
E. T=10yr, v=0.8c

The Attempt at a Solution

the time is the proper time interval for each of them. Should it be just C=A > B=E> D?

 

[J Hann]

Check the graph for the time dilation factor, we'll just call this D for convenience.
For v (A) = .4 c we have D = .9
and for V(C) = .8c we have D = .6
Obviously A does not equal C in terms of time dilation.
Note that the proper time is measured by a single clock place (during the journey).
So the proper time is measured by the clock on the spaceship.
Then T = T0 / D where T0 is the proper time as measured on the spaceship and T is
the corresponding time interval as measured by an observer on earth.
Don't confuse this with the T given in the problem which is T0 the proper time.

 

[kolua]

Check the graph for the time dilation factor, we'll just call this D for convenience.
For v (A) = .4 c we have D = .9
and for V(C) = .8c we have D = .6
Obviously A does not equal C in terms of time dilation.
Note that the proper time is measured by a single clock place (during the journey).
So the proper time is measured by the clock on the spaceship.
Then T = T0 / D where T0 is the proper time as measured on the spaceship and T is
the corresponding time interval as measured by an observer on earth.
Don't confuse this with the T given in the problem which is T0 the proper time.

so the answer would be C>A>E>B>D in this regard then?

 

[J Hann]

so the answer would be C>A>E>B>D in this regard then?

I would agree with that answer.

 

[kolua]

I would agree with that answer.

wouldn't this answer be the same with the one for question :Rank these quintuplets on the basis of the year on Earth when they return from their journey. ?
I just thought this might be strange.

 

[J Hann]

wouldn't this answer be the same with the one for question :Rank these quintuplets on the basis of the year on Earth when they return from their journey. ?
I just thought this might be strange.

I agree with the order that you posted!