Solve Length Contraction Homework: Find v

AI Thread Summary
To solve for the speed v of a spaceship experiencing length contraction, the equation L = L1√(1 - v²/c²) is used, where L is the observed length (300 m) and L1 is the proper length (356 m). By rearranging the formula, v can be expressed in terms of c by letting x = v/c and rewriting the equation as L/L1 = √(1 - x²). Squaring both sides leads to 1 - (L/L1)² = x², allowing for the calculation of x. The final expression for x is x = √(1 - (L/L1)², which provides the correct solution for v in terms of c. This method effectively resolves the length contraction problem.
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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.
 
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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.
 
L/L1=sqrt(1-x^2)
(L/L1)^2=1-x^2
1-(L/L1)^2=x^2
x=sqrt(1-(L/L1)^2)
 
Good. That should you get you the correct answer.
 

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