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Question: Tom leaves earth in a rocket on 1st Jan 2024. He accelerates immediately to 75% the speed of light. He maintains that consistent speed for his entire journey. He returns to earth on 31st Dec 2024 and immediately decelerates to 0. How many earth years will he have aged while he was away?
This question refers to the concept of time dilation in Einstein's theory of special relativity. The formula to calculate time dilation is t = t0/(sqrt(1-(v^2/c^2))), where t is the time experienced by the observer moving at speed v, t0 is the time experienced by the stationary observer, v is the speed of the moving observer, and c is the speed of light. Here, v = 0.75c (75% of the speed of light) and t0 = 1 year (the time experienced by someone on Earth). Hence, t = 1/(sqrt(1-(0.75c)^2/c^2)) = 1/(sqrt(1 - 0.75^2)) t = 1/sqrt(0.4375) = 1.5118579 So, for Tom, roughly 1.51 years will have passed. Thus, Tom will have aged about 1.51 earth years during his journey away. Please note that this is a simplified explanation and actual calculations may involve more complex adjustments depending on factors such as changing speeds, gravity, and other relativistic effects.
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