Naked Science Forum

Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Dlarah on 29/12/2008 22:40:38

Title: How are velocities added together?
Post by: Dlarah 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)

Title: Re: How are velocities added together?
Post by: lightarrow on 29/12/2008 23:00:50

Quote from: Dlarah 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)

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/c²)

which reduces to the simpler formula V_BE - V_FB when both speeds are little with respect to c.

Title: Re: How are velocities added together?
Post by: Dlarah 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.

Title: How are velocities added together?
Post by: Dlarah 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.

Title: How are velocities added together?
Post by: lightarrow on 10/01/2009 22:31:36

Quote from: Dlarah 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.

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.