# Homework Help: Length Contraction spaceship Problem

1. Mar 9, 2010

### hbrinn

1. The problem statement, all variables and given/known data
A spaceship passes you at a speed of .750c. You measure its length to be 28.2 m. How long would it be when at rest?

2. Relevant equations
I think the equation that is relevant is L=L(sub0)xsqrt(1-v^2/c^2)

3. The attempt at a solution
L=28.2xsqrt(1-(.75^2))=18.65m
Apparently, the answer is 42.6 m. I can't even imagine how to get 42.6 from that.

2. Mar 9, 2010

### collinsmark

I think you just got your variables swapped. If you are using

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

then $$L$$ is 28.2 m, and you need to solve for $$L_0$$, the length when the relative velocity is 0. $$L$$ is the length when traveling at speed $$v$$.

3. Mar 9, 2010

### hbrinn

Then by that logic isn't the answer 64.457?

I did 28.2=L(1-.75^2). Is that wrong?

4. Mar 9, 2010

### collinsmark

You forgot to take the square root. :tongue2:

5. Mar 9, 2010

### vela

Staff Emeritus
You forgot the square root.

6. Mar 9, 2010

### hbrinn

Yay! Thank you very much!