I've tried for hours to solve for v, but can't get the rearranging right.

I'm using

L= Lo sqrt 1- v^2/c^2

Can anyone suggest the first couple of steps?

I can get the answer by the way, by substituting values 'til I get the contracted length. Original and final length are given.

Thanks

assistance needed

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I am not familiar with this formula, but I can help with the manipulation.

L= Lo sqrt 1- v^2/c^2 or
L= Lo √( 1- v^2/c^2)
square both sides
L^2 = (Lo)^2(1-v^2/c^2)
L^2/(Lo)^2 = 1 - v^2/c^2
multiply both sides by c^2
c^2L^2/(Lo)^2 = c^2 - v^2
rearrange:
v^2 = c^2 - c^2L^2/(Lo)^2
v = √[c^2 - c^2L^2/(Lo)^2]

actually v would be +/- but I would guess you only wanted the positive result of v

To rearrange the equation L = L₀√(1 - v²/c²) to solve for v, you can start by squaring both sides of the equation:

(L/L₀)² = (1 - v²/c²)

Next, you can multiply both sides by L₀²:

L² = L₀²(1 - v²/c²)

Expanding the equation:

L² = L₀² - L₀²(v²/c²)

Rearranging the terms:

L₀²(v²/c²) = L₀² - L²

Now, divide both sides by L₀²:

(v²/c²) = (L₀² - L²) / L₀²

Finally, take the square root of both sides:

v/c = √[(L₀² - L²) / L₀²]

To solve for v, multiply both sides by c:

v = c * √[(L₀² - L²) / L₀²]

Now, you can substitute the given values for L₀, L, and c into the equation to determine the value of v.