Quote:
Originally Posted by snas
Thanks for the comments Steve and Rob. Just wondering, at what speed does the equation change from the intuitive equation u = u' + v to the special relativity equation u=(u'+v)/(1+(u'v/c^2))
Stuart
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Hello Stuart,
As Rob points out it is based on the u'v/c^2 term. It depends on how accurate you want to be.
If the 2 particles approach each other at say 100km/hr or 0.28 km/sec, uv'/c^2 becomes (0.28*0.28)/300000^2 = 0.000000000000871. For all intents and purposes the uv'/c^2 term is zero and we use u=u'+v.
Even for particles travelling towards each other at 0.1c or 30000 km/sec, the uv'/c^2 term is small.
(0.1c*0.1c)/c^2 = 0.01.
u=u'+v is still a good approximation.
u=u'+v
= 0.2c
u=(u'+v)/(1+(u'v/c^2))
=0.2c/(1.01)
=0.198c
Regards
Steven