Here is a web page adding speeds v and w.pitches are in the same direction the train is moving, the ball will actually be moving at V = 150 mph relative to the ground. The law of addition of velocities in the same direction is relatively straightforward, V = w + v. But according to Einstein’
https://demonstrations.wolfram.com/EinsteinsFormulaForAddingVelocities/
Suppose a baseball team is traveling on a train moving at v = 60 mph. The star fastball pitcher needs to tune up his arm for the next day’s game. Fortunately, one of the railroad cars is free, and its full length is available. If his w = 90 mph
Unquote.
Lets say the speed limit on the track is c = 120 miles per hour. Nothing on track goes faster than speed-c, not even the baseball.
Use ( 5 /4 ) for dimensionless reduction factor greater than 1.
V = ( 60 mph + 90 mph ) / ( 5 /4 ) = 120 mph
60 mph-train + 60 mph-bball = 120 mph
30 mph-train + 90 mph-bball = 120 mph
48 mph-train + 72 mph-bball = 120 mph
The last option is what you might call “symmetric.”
V = 60 / ( 5 / 4 ) + 90 / ( 5 / 4 ) = 120
Einstein-EDoMB-1905-Section §5, quote:
“It is worthy of remark that v and w enter into the expression for resultant velocity in a symmetrical manner.”
The train is going down the track at 60 mph. Somebody decides to toss a baseball. The train must slow down to 48 mph.
Gimme a break !
You would need to use the equivalent of the relativistic speed
combination formula, which is w=(u+v)/(1+uv/c²). For your 60 mph train
and 90 mph fastball, it would be w=(60+90)/(1+(60*90/(120*120))) or
150/(1+5400/14400) or 150/(1+0.375) or 109.0909... mph seen from the ground.
Sci/phys no longer works for me as a web page so I am throwing in the towel.
Google’s blogspot works, at least for now.
https://dibdeck.blogspot.com/
The symmetry problem is not 150 → 109 versus 150 → 120. Who cares?
Problem: Do you cut back one or both speeds v and w?
Cutting train speed-v when baseball mass is negligible makes no sense.
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