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This is chapter 37 problem number 10.
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We have a meter stick.
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The length of the meter stick is given to us as it's moving at a very high speed.
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So it's 0 .348 meters.
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And it's proper length, meaning the length at rest is l -nutt.
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It's a meter stick, so it's a meter long.
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And we are asked to calculate what speed the meter stick moving the meter stick is moving relative to us now um as you know the equation that we have for the length that we have at motion with respect to the length that is at rest is all we need to do is divide the length at rest by gamma factor here gamma factor is going to be one over square of one minus v squared over c square, this speed, relative to the speed of life, right? so all we need to do is actually isolate this v out of that equation.
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Now going back here, then l over l0 is going to give us one over gamma.
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And if you look at this expression, then from here, one over gamma is going to be 1 minus v squared over c squared.
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So we can put that here, 1 minus v squared over c squared.
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Now what we need to do, we need to get rid of the square root, so let's square both sides of this equation.
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So we're going to have l over l not squared equals to 1 minus v squared over c squared.
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Now we want to isolate this term where we have the v.
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So v squared over c squared is going to be 1 minus l over l not squared...