An engineer is part of a mission to travel to a system of planets 6.8 light years away. She will travel at a speed of 0.9c. Her twin brother who is part of the settlement crew will leave at the same time, but will travel at a speed of 0.4c. Calculate the age difference between the twins when the brother arrives and determine who will be older.
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Help with time dilation question :( (1 Viewer)
- Thread starter glauben
- Start date
This should be right..
Apply the length contraction formula to both scenarios (L1 is girl, L2 is boy):
L1 = 6.8√(1-0.9^2)
L1 = 2.96 light years
L2 = 6.8√(1-0.4^2)
L2 = 6.23 light years
Now convert this distance into metres by multiplying by (9.46 x 10^15):
L1 = 2.80 x 10^16
L2 = 5.90 x 10^16
Rearrange the speed = distance/time formula and find time:
T1 = (2.80 x 10^16)/(0.9 x 3 x 10^8)
T1 = 103703703.7 seconds
T1 = 3.29 years
T2 = (5.90 x 10^16)/(0.4 x 3 x 10^8)
T2 = 491666666.7 seconds
T2 = 15.59 years
So now the difference in their ages is 15.59 - 3.29 = 12.3 years
The brother is older because he takes longer to get there.
Hope that helps
Apply the length contraction formula to both scenarios (L1 is girl, L2 is boy):
L1 = 6.8√(1-0.9^2)
L1 = 2.96 light years
L2 = 6.8√(1-0.4^2)
L2 = 6.23 light years
Now convert this distance into metres by multiplying by (9.46 x 10^15):
L1 = 2.80 x 10^16
L2 = 5.90 x 10^16
Rearrange the speed = distance/time formula and find time:
T1 = (2.80 x 10^16)/(0.9 x 3 x 10^8)
T1 = 103703703.7 seconds
T1 = 3.29 years
T2 = (5.90 x 10^16)/(0.4 x 3 x 10^8)
T2 = 491666666.7 seconds
T2 = 15.59 years
So now the difference in their ages is 15.59 - 3.29 = 12.3 years
The brother is older because he takes longer to get there.
Hope that helps
Last edited:
Fizzy_Cyst
Well-Known Member
^^^
You have forgotten to take into account the amount of time which the engineer waits on the planet for her brother to arrive! (Don't feel bad, the marking scheme forgot it also!)
You have forgotten to take into account the amount of time which the engineer waits on the planet for her brother to arrive! (Don't feel bad, the marking scheme forgot it also!)