Ancient astronaut theorist Nutter B. Butter claims that the Caloprians from planet Calop, 30 light years away and at rest with respect to the Earth, wiped out the dinosaurs. The iridium layer in the crust, he claims, indicates spaceships with the fuel necessary to travel at 30% of the speed of light here and back, and that their engines allowed them to instantaneously hop to this speed. He also says that Caloprians can only reproduce on their home planet. Call the minimum life span, in years, of a Caloprian, assuming some had to reach Earth to wipe out the dinosaurs, $T$. Assume that, once a Caloprian reaches Earth, they instantaneously wipe out the dinosaurs. Then, $T$ can be expressed in the form $m\sqrt{n}$, where $n$ is not divisible by the square of a prime. Find $m+n$. [i](B. Dejean, 6 points)[/i]

Let the rest energy of a particle be $E$. Let the work done to increase the speed of this particle from rest to $v$ be $W$. If $ W = \frac {13}{40} E $, then $ v = kc $, where $ k $ is a constant. Find $10000k$ and round to the nearest whole number. [i](Proposed by Ahaan Rungta)[/i]