Question

Two students, Nora and Allison, are both the same age when Allison hops aboard a flying saucer and blasts off to achieve a cruising speed of 0.830c for a 29.5 year-round trip (according to Allison). Neglecting the brief time periods required for the acceleration of the ship during blastoff and turnarounds, find the difference in age between Nora and Allison when they are reunited.

Answer 1

23.38 years

Step-by-step explanation:

Speed of Allison = 0.83 c = v

Time passed according to Allison = Δt = 29.5 years

Time dilation

`\Delta t'=\frac{\Delta t}{\sqrt{1-(v^2)/(c^2)}}\\\Rightarrow \Delta t'=\frac{29.5}{\sqrt{1-(0.83^2c^2)/(c^2)}}\\\Rightarrow \Delta t'=(29.5)/(√(1-0.83^2))\\\Rightarrow \Delta t'=52.88\ years`

For Nora 52.88 years would have passed

So, their age difference would be 52.88-29.5 = 23.38 years