I’m confused

Nothing can travel faster than the speed of light.  We all know that, but how about the speed of a ping pong ball? What if someone hits a ping pong ball right at you?  It will be traveling at a speed of about 50mph.  But wait!  What if the person hitting the ping pong ball is in a train speeding toward you at 100mph?  Now the ping pong ball is traveling toward you at a speed of 150mph. The speed of an object isn’t an absolute.  Speed only means something when it is compared to some other object.  Turn our train around and make it travel away from you at 100mph.  Have our ping pong player hit the ball the other direction too, and now the ball is traveling away from you at 150mph. But what if the train can travel at say, just over half the speed of light?  Okay, maybe it’s not really a train, maybe we could just call it a particle.  So fire a particle away from you at just over half the speed of light.  At the same moment that happens, jump on your train going just over half the speed of light the other direction.  What happened?  How fast did the particle just go compared to you? Or did it even happen?  

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