Suppose you are planning a trip in which a spacecraft is totravel at a constant velocity for exactly twelve months, asmeasured by a clock on board the spacecraft, and then return homeat the same speed. Upon return, the people on earth will have agedexactly one hundred twenty-five years. According to specialrelativity, how fast must you travel? (Express your answer to atleast 5 significant figures as a multiple of c -- for example,0.95585c.)
Here is what I did:
t' = 12 months
t = 125 years = 1500 months
t/t' = â(1-(v2/c2))
(12/1500)2 =(â(1-(v2/c2)))2
6.4x10-5 =1-(v2/c2)
0.999936 = (v/c)2
v/c = â(0.999936)
v = 0.999968c
I used 0.99997 and 0.99996 (five significant figures)... butnothing is working. I'm not sure if I missed something or did thealgebra wrong?
Suppose you are planning a trip in which a spacecraft is totravel at a constant velocity for exactly twelve months, asmeasured by a clock on board the spacecraft, and then return homeat the same speed. Upon return, the people on earth will have agedexactly one hundred twenty-five years. According to specialrelativity, how fast must you travel? (Express your answer to atleast 5 significant figures as a multiple of c -- for example,0.95585c.)
Here is what I did:
t' = 12 months
t = 125 years = 1500 months
t/t' = â(1-(v2/c2))
(12/1500)2 =(â(1-(v2/c2)))2
6.4x10-5 =1-(v2/c2)
0.999936 = (v/c)2
v/c = â(0.999936)
v = 0.999968c
I used 0.99997 and 0.99996 (five significant figures)... butnothing is working. I'm not sure if I missed something or did thealgebra wrong?
