# I have a homework question on relativity which i can't figure out, i'd like some help

1. Apr 19, 2012

### SuperNova1

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

Moe measure the length of his space ship as 350 m. Joe observes this space ship as it flies by his position and measures that it took 0.700 s to pass through. What is the speed of the spaceship?

l': the length of the spaceship as measured by MOE = 350m
t: the time as measured by JOE = .7 x10^-6

2. Relevant equations
i'm not positive on the equations obviously speed = distance/time won't work as joe will not measure the length of the spaceship the same as moe will
i found an equation on the relativity of length and how it changes in relation to the observer outside the moving object which was ..... change in t1 = L'/(c-u)
but i'm not too sure whether it's anywhere close to the correct equation

3. The attempt at a solution
i tried distance/time 350/.7*10^-6 = 5*10^8 which can't be right for obvious reasons as the spaceship cannot travel faster than the speed of light
then i tried 0.7*10^-6 = 350/3*10^8 - u
350 = 0.7*10^-6(3*10^8 - u)
350/.7*10-6= 3*10^8 - u
5*10^8 - 3*10^8 = -u
u = -2*10^8
and this answer doesn't look good either
thank you to anyone who can help

2. Apr 19, 2012

### HallsofIvy

Staff Emeritus
Re: I have a homework question on relativity which i can't figure out, i'd like some

You appear to be using length as measured in one reference frame (Moe's) and time as measured in another (Joes's). You can't use those together.

What you can do, I think, is this- let v be Moe's speed relative to Joe. Then the length as measured in Joe's reference frame is $350/\sqrt{1- v^2/c^2}$. Now, you can say that "speed" is "distance divided y time"- $v= 350/.7\sqrt{1- v^2/c^2}= 500/\sqrt{1- v^2}$ so that $v\sqrt{1- v^/c^2}= 350$. Solve that for v.

3. Apr 19, 2012

### rude man

Re: I have a homework question on relativity which i can't figure out, i'd like some

The space ship from Joe's view contracts. You have it expanding. (Lorentz contraction).
Just multiply 350m by √(1 - v2/c2) instead of dividing.

So the idea is: compute the length of the spaceship as measured by Joe, divide by Joe's time, and that will give the (contracted) length as seen by Joe.

4. Apr 19, 2012

### SuperNova1

Re: I have a homework question on relativity which i can't figure out, i'd like some

Thank you for all your help guys i did it again and got a value of 0.988c or 2.994*10^8 which sounds right to me as the lecturer told us it was close to the speed of light, thank you again