Question

The Hypersonic Technology vehicle 2 (HTV-2) is an experimental rocket vehicle capable of travelling at 21000 km/h (5830 m/s). If an electronic clock in the HTV-2 measures a time interval of exactly 1s duration, what would observers on Earth measure the time interval to be? 

Answer 1

Given quantities:

$\tau=1s \space\space\space v = 5830 \frac{m}{s} \space\space\space c = 3 * 10^ 8\frac{m}{s}$

$t = \gamma\tau = \large\frac{\gamma}{\sqrt{1-\large\frac{v^2}{c^2}}}=\frac{1s}{\sqrt{1-\frac{5830^2}{(3*10^8)^2}}}$ $=1s+1.89*10^{-10}s$