# 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.

Orodruin
Staff Emeritus
Homework Helper
Gold Member
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
Staff Emeritus
Homework Helper
Gold Member
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
Staff Emeritus
Homework Helper
Gold Member
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
Staff Emeritus
Homework Helper
Gold Member
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
Staff Emeritus
Homework Helper
Gold Member
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