Nice. Could a baseball pitched at 90% the speed of light from [anywhere that could produce such a speed] make it to Earth and impact? What can cause chunks of matter to travel this fast?

Could one make it to Earth and impact? The universe is very large, so it's a possibility, but space is very big and very empty, so we'd have to get very very very very unlucky for that to happen. But supernova explosions, pulsars and neutron stars, gamma-Ray bursts, supermassive black holes, and (theoretical) dark matter annihilation could all do it.