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PHYSICS HELP! (Time Dilation) According to special relativity, how fast must you travel?

Suppose you are planning a trip in which a spacecraft is to travel at a constant velocity for exactly twelve months, as measured by a clock on board the spacecraft, and then return home at the same speed. Upon return, the people on earth will have aged exactly one hundred twenty-five years. According to special relativity, how fast must you travel? (Express your answer to at least 5 significant figures as a multiple of c -- for example, 0.95585c.) _________c

Public Comments

1. This is a 2 year trip right? One year out then one year back? Assuming so: Time dilation factor = d = 125/2 = 62.5. Dilation factor as a function of speed is: d = 1/sqrt(1-v^2). Solving for v: v = sqrt(1-1/d^2) = sqrt[1-1/(62.5)^2] = 0.999872c
2. The total travel time is 2 years on your clock. On Earth 125 years will have passed. The gamma factor is thus: gamma = 125/2 The gamma factor is given in terms of the velocity by: gamma(v) = 1/sqrt(1 - v^2/c^2) So, v = 0.999871992 c
3. We use the formula, t(v) = t(0)sqrt{1 - (v/c)^2}. t(0)=125 yrs t(v)=1 yr 1 = 125sqrt{1 - (v/c)^2} sqrt{1 - (v/c)^2} = 1/125 1 - (v/c)^2 = 1/15625 = 0.000064 (v/c)^2 = 0.999936 v/c = sqrt(0.999936) = 0.9999679 v = 0.9999679995