# How fast must a meter stick be moving if its length is....

## Homework Statement

How fast must a meter stick be moving of its length is measured to shrink to 0.500 meters?

## Homework Equations

v/c = sqrt(1 - (1/L)^2) = sqrt(1 - 1/4) = sqrt(3/4) = sqrt(3)/2 or use v = sqrt(3)c/2

## The Attempt at a Solution

(squrt 3c/2) = squrt 450000000 = 21213.203 = 21213.2 km/sec.

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Orodruin
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You have taken sqrt(3c/2) instead of sqrt(3) c/2 ... The square root of a velocity can never be a velocity.

So it's (sqrt of 3)/(c/2)??

Orodruin
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No, your original math when arriving at sqrt(3) c/2 was correct. What you did not do correctly was inserting numbers into this formula. There is a difference between sqrt(3) c/2 and sqrt(3c/2)...

So my answer is correct? I still don't understand.

Orodruin
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No, it is not correct. What part of sqrt(3) c/2 is not equal to sqrt(3c/2) do you find confusing.

After I take the square root of 3, I multiply that by the c/2??

Orodruin
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Yes, this is what your expression tells you to do.

1.7320 times c/2 = 1.7320 times 150,000,000 = 2.598E8 = 2.598 X 10^8 km/sec

Orodruin
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Better, but as you are giving the speed of light with one significant digit, you really should not have four significant digits in your answer.

1.7 times 150,000,000 = 2.55E^8 = 2.5 X 10^8 km/sec.

Orodruin
Staff Emeritus