In a basic world, YES.
In a slightly more complicated world with wind resistance, YES, RELATIVE TO THE GROUND, ASSUMING HE THREW IT IN THE DIRECTION THE TRAIN WAS GOING, but it immediately starts slowing down.
In a massively more complicated (but technically more accurate) world, it’s going about 149.9999999999 mph.
Due to relativity, speeds don’t sum linearly.
Feel free to ask questions if you have them.
Short answer yes. Depending on your frame of reference, however the speed is different. For example, if someone was standing on the train and got hit with the ball, it would be with the momentum of a 100MPH pitch hitting him. If the ball hit someone standing on a platform near the train it would be with the momentum of a 150MPH pitch
It depends on what your perspective is. Speed is only meaningful when it’s relative to something else. From the perspective of someone standing still and watching the train go by, yes. From the perspective of the person throwing the ball, no, the ball is only going at 50mph relative to the pitcher. Both are equally correct. This is actually a concept that’s really important in and fundamental to Einstein’s special relativity.
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