- #1

Yosty22

- 185

- 4

## Homework Statement

You are exploring a newly discovered planet when a colleague contracts a deadly alien virus. Left untreated, it will probably kill him in 5 days, but the nearest medical station is 10 light-days away! How can you get him there in time?

## Homework Equations

Δt

_{p}=L/v

L=L'/\gamma

\gamma = 1/sqrt(1-v^2/c^2)

## The Attempt at a Solution

Intuitively, I read this question and concluded that you could not do it. How could you possibly go 10 light-days in only 5 days? However, I tried to work through it anyway. Given the equation for Δt

_{p}(proper time), I substituted some other values. The L term represents the contracted length, so I replaced L with L'/\gamma into the equation Δt

_{p}=L/v. This gave me Δt

_{p}=[(L'(1-v^2/c^2)^.5)]/v. Doing quite a bit of algebra, I ended up solving for v (the velocity of the ship) and got v=(L'^2/Δt

_{p}^2)^.5.

I converted 5 days into seconds (so that I could work in meters/second) and got it to be 432,000 seconds. I said that this should be my Δt

_{p}term because this is the time measured on the ship, so you need it to be 5 days to save the other astronaut. I then converted 10 light days into meters (again, to keep things simpler for me). I found 10 light days to be 2.592E14m. Plugging this into my previously derived equation, I got the speed necessary for the ship to reach the medical station (including time dilation and length contraction) to be 2c.

Is this supposed to happen, or should there be a true answer that would allow me to get the other passenger to travel 10 light days in a 5 day span (in his frame of reference)?

Any help would be much appreciated.

Thank you.