Can someone help me with this relativity problem? For a.) I got that she aged 6
ID: 2075332 • Letter: C
Question
Can someone help me with this relativity problem? For a.) I got that she aged 6 years and for b.) Her friend aged 60 years. Not sure if this correct. Gamma 10 which corresponds to a v 0.995c. Suppose Thelma was 20 years old when she started traveling to planet Zork at this speed. Zork is 30 light years away, and is not moving with respect to earth. She then turned around and immediately came home at the same speed. a) How old was she when she got home? b) Her friend Louise was also 20 when Thelma left. How old is shewhen Thelma gets home? c) Louise sent a radio message to Zork when Thelma left. How old is she when (from her point of view) the message arrives at Zork? d) How old is Thelma when (from her point of view) the message arrives at Zork?Explanation / Answer
a] For Thelma, the distance between Earth and Zork is Lorentz contracted so, L' = L/10
total distance traveled by her = 2L' = 2L/10
v = 0.995c
so assuming she instantaneously changed her speed and turned around from Zork, the time taken as measured by Thelma will be:
t = 2L'/v = 6.03 years.
so, when Thelma returned home, her age will be: 20 + 6.03 = 26.03 years.
b] Louise's time must be dilated by a factor of 10
so, T = 20 + (10 x 6.03) = 80.3 years.
c] Speed of the message = v = c
time taken by the signal to reach Zork = t = L/v = 30 years
so, Louise's age at this instant will be: 20 + 30 = 50 years.
d] Thelma's age when this signal reaches Zork will be: 20 + (50/10) = 25 years.