If a person lives on average 100 years in his rest frame, determine how long he lives in the earth frame if he spends his entire life on a spaceship travelling at 60 % of the speed of light.

Step-by-step solution

The proper time interval, which is the lifetime measured in the person's rest frame, is t₀ = 100 years. The velocity of the spaceship relative to the Earth frame is v = 0.6c . Using the time dilation formula, the lifetime measured in the Earth frame is given by: t = t₀ 1 - v^2 c^2 Substituting the given values: t = 100 1 - (0.6)^2 t = 100 1 - 0.36 t = 100 0.64 t = 100 0.8 = 125 years