If i stand on a boat, which is traveling in 60 m/h and shooting a football at 60 m/h in the way the stern is pointing (thus in the opposite direction of the boats traveling speed) What velocity will this football have? And is there an equation for this?

(Hope this haven't been mentioned before. Because I've looked but I didn't find anything)

I know it will sound strange to you, but you have to think in this terms:

"If I stand on a boat, which is traveling in 60 m/h

*with respect to...* (fill in with what interests you, e.g. the Earth's surface) and shooting a football at 60 m/h

*with respect to...* (e.g. : the boat) in the way the stern is pointing, thus in the opposite direction of the boats traveling speed. What velocity will this football have

*with respect to...*(e.g. : the Earth's surface)?

V

_{BE} = Boat's velocity with respect to Earth

V

_{FB} = football's velocity with respect to Boat

V

_{FE} = football's velocity with respect to Earth

then: V

_{FE} = V

_{BE} - V

_{FB} = 60 - 60 = 0.

In the relativistic case (certainly not with boats and footballs!) you will instead have:

V

_{FE} = (V

_{BE} - V

_{FB})/(1 -V

_{BE}*V

_{FB}/c

^{2})

which reduces to the simpler formula V

_{BE} - V

_{FB} when both speeds are little with respect to c.