Detailed solution please? Fraternal twins Speedo and Notso travel to a planet 20

Question

Detailed solution please?

Fraternal twins Speedo and Notso travel to a planet 20 light years from the earth. Speedo’s spaceship moves at 0.95c relative to the earth and Notso travels at the relatively slow speed of 0.8c. How will the twins differ in age when both have arrived at the planet? (We assume rapid acceleration and deceleration.)

a. Speedo will be 8.43 years younger than Notso.

b. Speedo will be 6.57 years younger than Notso.

c. They will be the same age.

d. Speedo will be 4.48 years younger than Notso.

Explanation / Answer

Speedo speed = 0.95c

time to reach the planet = 20/0.95 = 21.053 Yrs relative earth observer

Notso speed = 0.8c

time to reach planet = 20/0.8 = 25 Yrs relative earth observer

we ingnore the acceleration and deacceleration times.

gama(speedo) = 1/sqrt(1-0952) = 3.2027

speedo clock will count his travel time as = 21.053/3.2027 = 6.5735 yr

Notso wil arrive after (25.0-21.053) = Yrs

Speedo will be at rest after reaching the planet and his clock will count same as on earth

Time read by Speedo until Notso arrives = 6.5735 + 3.947 = 10.5205 Yr

gama of Notso = 1/sqrt(1.0.82) = 5/3

Notos clock will read as 25*3/5 = 15 Yrs by the time he arrives at the planet

Speedo will be younger by 15.0 -10.52 = 4.48 Yrs.

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