# Homework Help: Twin Paradox-esque Problem

1. Mar 6, 2012

1. The problem statement, all variables and given/known data

A friend of yours who is the same age as you travels to the star Alpha Centauri, which is 4 light· year away, and returns immediately. He claims that the entire trip took just 6 years. How fast did he travel? How much older are you than him when he returns?

2. Relevant equations

$\Delta t$ = $\frac{\Delta t_0}{\sqrt{1-\frac{u^2}{c^2}}}$

$L = L_0 \sqrt{1-\frac{u^2}{c^2}}$

Speed = Distance/Time
$\vec{u} = \frac{2L_0}{\Delta t_0}$

I'm not really sure if $\vec{u}$ is equal to that or the contracted length/dilated time....

3. The attempt at a solution

My original attempt to solve this involved simply dividing the time for the round trip in terms of meters (8 light years ~ $8*10^{16}$ meters, and the time was 6 years, which I converted to seconds).

This game me an answer of approximately 1.4c, which seems to be clearly impossible. I'm assuming I'm missing something about time dilation and length contraction, but I can't seem to figure out how to use either of these without knowing what either the speed is or the dilated time/contracted length. If I can find the speed, it seems relatively straight forward from there, just use time dilation and subtract the dilated time from the proper time to see how much the person on Earth had aged.

2. Mar 6, 2012