SR quiz!

[jdavel]

A train is moving to the right at v=.5c. Someone standing on the train throws a baseball forward (to the right) at u'=.99c (relative to him). Relative to somone on the ground, the ball appears to be traveling at a speed u which is slightly faster than .99c, but still less than c.

What if the guy on the train throws the ball backwards (u'=-.99c)? Now what speed does the guy on the ground see? Try to get the approximate answer without looking at the velocity addition formula.

[NateTG]

What if the guy on the train throws the ball backwards (u'=-.99c)? Now what speed does the guy on the ground see? Try to get the approximate answer without looking at the velocity addition formula.

My best guess is a speed of slightly less than .99c.

A quick thought on the topic:
Let's say we've got an explosion pushing two balls of equal mass out of a pipe. Then linear momentum is conserved if both balls go out of the pipe in opposite directions at .99c. Now, if we put this double-sided gun on the relativistic train, the outside observer will still need to have linear mometum conserved, and we know that in a absolute sense the momentum change from .5c to .99c is much much larger than the momentum from 0c to .5c. Therefore, the ball will be seen as traveling backwards at more than .5c.