Based on experiments in your lab, you know that a certain radioactive isotope has a half$-$life of $2\mathrm{.}15s.$ As a high$-$speed spaceship passes your lab, you measure that the same isotope at rest inside the spaceship takes $3\mathrm{.}85s$ for one$-$half of it to decay.

What is the half$-$life $t_{\frac{1}{2}}$ of the isotope, in microseconds, as measured by an astronaut working inside the spaceship?

$t_{\frac{1}{2}}=$

$s$

How fast $v$ is the spaceship traveling relative to Earth in multiples of $c?$

$v=$

c