Neutrons have a proper half-life of 610 seconds. it has been theorized that extremely energetic neutrons could be produced by collisions of ultra-energetic protons (accelerated by an unknown mechanism) with nuclei. for a collection of neutrons to reach earth with 50% surviving, how close to the speed of light must their velocity be (i. e., what is c – v in m/s) if they are created near sagittarius a (black hole at the center of our galaxy), 25,000 light-years distant?

hint: the γ factor is extremely large so use an approximation of β for large γ