# The Naked Scientists Forum

#### Dlarah

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• Posts: 9
##### How are velocities added together?
« on: 29/12/2008 22:40:38 »
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)
« Last Edit: 01/01/2009 04:05:04 by chris »

#### lightarrow

• Neilep Level Member
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##### Re: How are velocities added together?
« Reply #1 on: 29/12/2008 23:00:50 »
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)?

VBE = Boat's velocity with respect to Earth
VFB = football's velocity with respect to Boat
VFE = football's velocity with respect to Earth

then: VFE = VBE - VFB = 60 - 60 = 0.

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

VFE = (VBE - VFB)/(1 -VBE*VFB/c2)

which reduces to the simpler formula VBE - VFB when both speeds are little with respect to c.
« Last Edit: 29/12/2008 23:09:09 by lightarrow »

#### Dlarah

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• Posts: 9
##### Re: How are velocities added together?
« Reply #2 on: 30/12/2008 00:11:06 »
Thank you very much Lightarrow!
I do understand much better now. I'm not that good at the "verbal" physics, but when I see an equation, like yours, I really understand... I'm wierd.

#### Dlarah

• First timers
• Posts: 9
##### How are velocities added together?
« Reply #3 on: 10/01/2009 22:04:47 »
Hi again!

I just want to check if i do understand...
We have two lightbeams that are moving away from eachother with me as an stationary observer in the middle. If they would be moving at 60m/s, the gap in between would increase with (approximately, Lorentzfactor is neglectable) 120m/s, right?

But if they were moving at the speed of light, would the gap increase with c or with 2*c?
Because in special relativity, lights velocity is equal to all observers, and because of the formula Lightarrow gave me I think it is c.

#### lightarrow

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##### How are velocities added together?
« Reply #4 on: 10/01/2009 22:31:36 »
Hi again!

I just want to check if i do understand...
We have two lightbeams that are moving away from eachother with me as an stationary observer in the middle. If they would be moving at 60m/s, the gap in between would increase with (approximately, Lorentzfactor is neglectable) 120m/s, right?

But if they were moving at the speed of light, would the gap increase with c or with 2*c?
Because in special relativity, lights velocity is equal to all observers, and because of the formula Lightarrow gave me I think it is c.
What you are discussing here is usually called "separation velocity" between two objects, which is not their relative velocity. The separation velocity doesn't correspond to a physical entity, it's only a mathematical object; between two opposite moving light beams is indeed 2c.
The physical entity velocity is defined in a different way. Let's assume we are talking about two starships moving very fast in opposite directions; to measure their relative velocity, you take a frame of reference co-moving with one of them and you measure the other's starship velocity. If you do it, what you get is:

V = (v1-v2)/(1-v1*v2/c2)

where v1 and v2 are the two starships' velocities (in algebric value, that is, if the starships are moving in opposite directions as in this case, one of them must be negative so at the end you actually make a sum, not a difference) measured from the initial frame of reference.

« Last Edit: 10/01/2009 22:44:10 by lightarrow »

#### The Naked Scientists Forum

##### How are velocities added together?
« Reply #4 on: 10/01/2009 22:31:36 »