The identical twins Speedo and Goslo join a migration from theEarth to Planet X.
ID: 1747996 • Letter: T
Question
The identical twins Speedo and Goslo join a migration from theEarth to Planet X. It is 19.0 ly away in areference frame in which both planets are at rest. The twins, ofthe same age, depart at the same time on different spacecraft.Speedo's craft travels steadily at 0.960c, and Goslo's travels at0.750c. Calculate the age difference between the twinsafter Goslo's spacecraft lands on Planet X.1 y
Which twin is the older? 2 Speedo
Goslo
They areactually the same age. 2 Speedo
Goslo
They areactually the same age. 2 Speedo
Goslo
They areactually the same age. 2
Explanation / Answer
Let the distance to planet X be S
Given S=19 light years
=19* 3x108 * 1 year
time taken for speedo's craft t= S/v
= ( 19 * 3x108 * 1 year) /0.960 c
= [19/0.96] 1 year Since c =3x108 m /s ------( 1)
time taken for goslo,s craft t ' = S /v '
= ( 19* 3x108 * 1 year)/ 0.750 c
= [19 / 0.75 ] 1year -----( 2)
relative time of Speedo's T = t ( 1 -(v/c)2)
= t ( 1 - (0.96c/c)2)
= 0.28 t
= 5.54.0 * 1year Since from eq ( 1)
relative time of Goslo's T ' = t ' ( 1 - (v '/c)2)
= t ' ( 1 - (0.750c/c)2)
=0.66 t '
= 16.75 * 1year Since from eq ( 2 )
Correction for "after Goslo's spacecraft lands on Planet X."
Since Speedo gets there in t01= S/v1= [19/0.96]Y he has to wait for Goslo to arrive.
Speedo' age will be equal to A + 5.54 years + waitfor Goslo time t' or
t' = t01 - t02 | =[19/0.75]Y - [19/0.96]Y = 5.541Y
Speedo' age = A + 5.54Y + 5.541Y= A + 11.08Y
Goslo's age = A + 16.75Y
Their age difference is A + 16.75Y - (A+ 11.08Y) = 5.668 Y
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