Answer to Question #172835 in Mechanics | Relativity for alto

Question

The USS Enterprise approaches the planet Alpha Centaury 4 at a speed of 0.800 c. Captain Kirk observes an airplane runway on the planet to be 2.00 km long. The air controller on the planet says that the runway on the planet is how long

Answer 1

$\text{according to the Lorentz contraction formula:}$

$l_1= l_0\sqrt{1-\frac{v^2}{c^2}}$

$\text{where:}$

$l_1- \text{the length of an object in the system of an observer }$

$\text{moving with speed }v$

$l_0=\frac{l_1}{\sqrt{1-\frac{v^2}{c^2}}}$

$l_0=\frac{2000}{\sqrt{1-\frac{0.64c^2}{c^2}}}=\frac{2000}{0.6}\approx3333m$

$l_0=3.3km$

Answer: 3.3 km - air traffic controller response