# Length Contraction spaceship Problem

## Homework Statement

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?

## Homework Equations

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

## 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.

collinsmark
Homework Helper
Gold Member

## Homework Statement

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?

## Homework Equations

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

## 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.

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 $$v$$.

Then by that logic isn't the answer 64.457?

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

collinsmark
Homework Helper
Gold Member
Then by that logic isn't the answer 64.457?

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

You forgot to take the square root. :tongue2:

vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
You forgot the square root.

Yay! Thank you very much!