Solve Length Contraction Homework: Find v

[sklotz]

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 356 m. Find v.

Homework Equations

L=L1sqrt(1-v^2/c^2)

The Attempt at a Solution

I have tried this by using the above formula. I plugged in 300 for L and 356 for L1 and I have tried it the other way as well where I plug in 300 for L1 and 356 for L. The answer is in terms of c. I only have one try left and don't understand what I am doing wrong.

 

[TSny]

You are looking for v in terms of c, which means that you are trying to find v/c. So, let x = v/c and write your equation as L = L1sqrt(1-x^2). Show us some of the details of how you would solve this for x.

 

[sklotz]

L/L1=sqrt(1-x^2)
(L/L1)^2=1-x^2
1-(L/L1)^2=x^2
x=sqrt(1-(L/L1)^2)

 

[TSny]

Good. That should you get you the correct answer.

 

[Nickie]

I would suggest checking your calculations and making sure you are using the correct units for velocity (m/s) and the speed of light (m/s). Also, make sure you are using the correct formula for length contraction, which is L=L0sqrt(1-v^2/c^2), where L0 is the rest length of the object. In this case, the rest length would be 356 m, not 300 m. Once you have the correct formula and values plugged in, you should be able to solve for v. If you are still having trouble, I would suggest seeking help from a tutor or your instructor for further clarification.