Question

When at rest, a ruler has a length of 12.0 inches. How fast (in m/s) must the ruler fly past you in order for it to shorten to 6.00 inches in length? Hint: to use scientific notation within Canvas, use e+ instead of 10^ (ex. 3.00×108 = 3.00e+8).

Answer 1

Answer:

2.598×$10^8 m/sec$

Explanation:

The length of the contraction is given by $l=l_0\sqrt{1-\frac{v^2}{c^2}}$ here $l_0$ is length of the ruler at rest which is given as 12 inches

l is the length of the ruler in moving condition which is given as 6 inches c is the speed of the light and v is the velocity of the ruler.

$l=l_0\sqrt{1-\frac{v^2}{c^2}}$

$\frac{l}{l_0}=\sqrt{1-\frac{v^2}{c^2}}$

$1-(\frac{l}{l_0})^2=\frac{v^2}{c^2}$

$1-(\frac{6}{12})^2=\frac{v^2}{c^2}$

$0.866=\frac{v}{c}$

$v=0.866\times 3\times 10^8=2.598\times 10^8 m/sec$