How Do You Calculate the Length of a Spaceship Using Relativity?

[tacosareveryyum]

Homework Statement

2 spaceships traveling in opposite directions pass one another at a relative speed of 1.25x18^8 m/s. The clock on one spaceship records a time duration of 9.1x10^-8 seconds for it to pass from the front end to the tail end of the other ship. What is the length of the second ship as measured from its own rest frame?

Homework Equations

lorentz transformations

The Attempt at a Solution

Okay so I am guessing that the second ship, as measured from its rest frame should be smaller that measured from the frame of the other ship.
I used the basic equation v=x/t and plugged in my relative speed of 1.25x10^8 m/s and my time 9.1x10^-8 s. I got 11.38 m as the length measured by the first ship. Then I used the lorentz transformation for length and found the length of the second ship to be 10.34 m.

 

[Gokul43201]

Homework Statement

2 spaceships traveling in opposite directions pass one another at a relative speed of 1.25x18^8 m/s. The clock on one spaceship records a time duration of 9.1x10^-8 seconds for it to pass from the front end to the tail end of the other ship. What is the length of the second ship as measured from its own rest frame?

Homework Equations

lorentz transformations

The Attempt at a Solution

Okay so I am guessing that the second ship, as measured from its rest frame should be smaller that measured from the frame of the other ship.

Should it? Who measures the proper length and who measures the contracted length?

I used the basic equation v=x/t and plugged in my relative speed of 1.25x10^8 m/s and my time 9.1x10^-8 s. I got 11.38 m as the length measured by the first ship.

This is correct.

 

[Doc Al]

I used the basic equation v=x/t and plugged in my relative speed of 1.25x10^8 m/s and my time 9.1x10^-8 s. I got 11.38 m as the length measured by the first ship.

Good. This is the length of the moving ship 2 as measured by ship 1.

Then I used the lorentz transformation for length and found the length of the second ship to be 10.34 m.

How did you do this? Do moving objects measure to be shorter or longer compared to their rest lengths?

Oops: Gokul43201 beat me!

 

[tacosareveryyum]

Okay, I am going in circles here. Isn't a measurement of length of the moving second ship going to yield a shorter length than the measurement made in the frame of the ship.

 

[tacosareveryyum]

Okay so the second ship should be measured to be 12.50 m as measured in its own rest frame.

 

[Doc Al]

Okay, I am going in circles here. Isn't a measurement of length of the moving second ship going to yield a shorter length than the measurement made in the frame of the ship.

Exactly.

Okay so the second ship should be measured to be 12.50 m as measured in its own rest frame.

Much better.

 

[tacosareveryyum]

thanks!