Calculating Velocity Using Length Contraction Formula in Relativity Theory

[sphys4]

Homework Statement

A spaceship moves past you at speed v. You measure the ship to be 300 m long, whereas an astronaut on the ship measures a length of 445 m. Find v.

The Attempt at a Solution

I tried to substitute my numbers into L1=Lsqrt(1/(v^2/c^2)) and keep getting a negative wrong answer!
445=300sqrt(1-(v^2/3E+8^2)) ... what am i doing wrong?

 

[Pi-Bond]

In your formula L (on the right hand side) is the proper length. Are you sure you have substituted the proper length correctly?

 

[sphys4]

In your formula L (on the right hand side) is the proper length. Are you sure you have substituted the proper length correctly?

Well L1 is supposed to be the length observed by an observer in relative motion with respect to the object, which would be 445?

 

[Pi-Bond]

But the astronaut is at rest relative to the spaceship. Who is the one measuring the moving spaceship?

 

[sphys4]

But the astronaut is at rest relative to the spaceship. Who is the one measuring the moving spaceship?

I guess that means i am, so i switch 300 and 445?

 

[Pi-Bond]

Yes. The right hand side of your equation deals with proper length, or the length measured by an observer in the rest frame of the object. (Astronaut in this case) The left side deals with what an observer in relative motion will measure as the length. (you in this case)

 

[sphys4]

Yes. The right hand side of your equation deals with proper length, or the length measured by an observer in the rest frame of the object. (Astronaut in this case) The left side deals with what an observer in relative motion will measure as the length. (you in this case)

aha i see, thank you so much!