Vector Qs: Football, Month, Book?

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In the discussion about identifying vectors, it is clarified that a vector must have both magnitude and direction. The quantities listed—number of people at a football game, number of days in a month, and number of pages in a book—are analyzed for their vector properties. It is concluded that the latter two quantities (days and pages) are purely magnitudes without direction. The first quantity's classification as a vector is debated, with humor suggesting that it could be considered a vector if expressed in directional terms. Ultimately, the consensus is that only the first quantity may have a directional aspect, while the others do not qualify as vectors.
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Physics Vectors Help!

Homework Statement



Which of the following quantities (if any) can be considered a vector? (Select all that apply.)

1. the number of people attending a football game

2. the number of days in a month

3. the number of pages in a book

4. none of the above

Homework Equations


A vector has Magnitude and Direction.

The Attempt at a Solution

 
Last edited:
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Hitsaguya said:

Homework Equations


A vector has Magnitude and Direction.

With this definition in mind, do any of those have both magnitude and direction?
 


Well #1 I am not sure about, but #2 adn #3 i kno don't deal with direction right? I'm pretty sure they all have magnitude because they all deal with numbers.
 
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Hitsaguya said:
Well #1 I am not sure about, but #2 adn #3 i kno don't deal with direction right? I'm pretty sure they all have magnitude because they all deal with numbers.

Yes 2 and 3 are just magnitudes.

But if you are confused with 1, just ask yourself this, do you normally say "the number of people attending a football game at 37 degrees to the x-axis"?
 


at 37 degrees to the x-axis

Maybe. who knows? :biggrin:
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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