Answer to Question #216603 in Mechanics | Relativity for Pearl

Question

A meter stick is projected into space at so a speed that it's length appears contracted to only 50cm. How fast is it going in m/s(2.6×10^8m/s)?

Answer 1

Solution.

$l_0=1m; l=0.5m;$

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

$l^2=l_0^2(1-\dfrac{v^2}{c^2})\implies v=c\sqrt{1-\dfrac{l^2}{l_0^2}};$

$v=3\sdot10^8\sqrt{1-0.25}=2.6\sdot10^8m/s;$

Answer: $v=2.6\sdot10^8m/s.$