# Length Contraction and special relativity

natxio

## Homework Statement

The dimensions of your friend’s spaceship are 100 meters in length, with a cabin width of 20
meters (i.e., you could approximate the main body of the ship as a cylinder with length 100
meters and diameter 20 meters). However, since your friend’s spaceship is speeding past you
at a relativistic velocity, you observe it to be highly foreshortened, with identical length and
width. At what speed is your friend traveling past you? Express your answer in units of the
speed of light.

## Homework Equations

length contraction equation:
Lmoving= Lrest x [ 1- v^2/ c^2] ^1/2

## The Attempt at a Solution

Lmoving= Lrest x [ 1- v^2/ c^2] ^1/2

solve for velocity --> v= c x [ 1- Lmoving^2/ Lrest^2] ^1/2

v= c x [ 1- 100m^2/ 100m^2] ^1/2
v= c x [ 1-1] ^1/2
v= c x [0] ^1/2
v= 0c

I don't know if I did this right, I don't know if I was supposed to include the width somewhere in here but if any of you guys can help me I would greatly appreciate it. Thank you!

## Answers and Replies

Science Advisor
Homework Helper
Well, you got that he is not really moving at all, so I guess that is not quite right.

Check again the value you have for Lmoving. The clue lies in the sentence:
However, since your friend’s spaceship is speeding past you at a relativistic velocity, you observe it to be highly foreshortened, with identical length and width.

Staff Emeritus
Science Advisor
Gold Member
You are looking for the velocity where your friend's ship looks as long as it is wide to you. If it is 20 meters wide, how short would it have to be contracted to lengthwise to fulfill this condition? ( At what speed will Lmoving be equal to the width of the ship.

natxio
thank you I understand it now, so Lmoving = 20m and Lrest= 100 meters and then I just solve for velocity. Thanks for all the help!!!!!!!

Science Advisor
Homework Helper
Are you sure the width is not contracted as well?