Projectile Motion: Solving Equations with Air Resistance

[Michaelbk]

Hi

Im trying to make an equation for a projectiles path, but this is only over a very short distance, so the projectiles curve aren't taken into account. I am including the air resistance.
This is what i have done:
m*dv/dt=-k*v2 Differential: dv/v2=-k*dt integrated: -1/v=-k*t+C when: t=0 og c=-1/v0 and we get: v=m*v0/(k*v0*t+m)
I have gotten some help doing this, but i am wondering if anyone could tell me if this is right. Another thing is that i seem to have forgotten "m", could anyone please tell me where "m" should be in the differentaded and integrated equation? i have a hard time explaing actually what i have done, but maybe you could help me.
By the way, I am from Denmark so sorry for my bad english.

Thanks
- Michael

 

[Michaelbk]

Anyone might be able to tell me where this: m*dv/dt=-k*v² comes from?

 

[tiny-tim]

Welcome to PF!

m*dv/dt=-k*v2 Differential: dv/v2=-k*dt integrated: -1/v=-k*t+C when: t=0 og c=-1/v0 and we get: v=m*v0/(k*v0*t+m)
I have gotten some help doing this, but i am wondering if anyone could tell me if this is right. Another thing is that i seem to have forgotten "m", could anyone please tell me where "m" should be in the differentaded and integrated equation?

Hi Michael ! Welcome to PF!

(use the X² tag above the reply field to make v² )

(and what's "og"? )

Yes, that's fine …

you lost the m (though somehow you put it back in the right position ) when you went from
m*dv/dt=-k*v²
to
dv/v²=-k*dt,

which should have been mdv/v²=-k*dt.

 

[Michaelbk]

Thanks :), i was wondering where this comes from too: m*dv/dt=-k*v²
Oh, and "og" is a danish word for "and", my bad

 

[tiny-tim]

Oh, and "og" is a danish word for "and", my bad

​

i was wondering where this comes from too: m*dv/dt=-k*v²

ah, i didn't see your second post

mmm … for me, it usually comes from the question …

if you want to find why air resistance is like that, http://en.wikipedia.org/wiki/Main_Page" is always a good place to start.

 

[Michaelbk]

I was meaning the formula m*dv/dt=-k*v² what's the original formula? or what is it calculated from? i mean dv/dt = a ... so might be F=m*a Newtons second law, but i don't know, i would appreciate some help here :)

 

[tiny-tim]

I was meaning the formula m*dv/dt=-k*v² what's the original formula? or what is it calculated from? i mean dv/dt = a ... so might be F=m*a Newtons second law, but i don't know, i would appreciate some help here :)

oh i see!

yes, it's good ol' Newton's second law … F = ma = mdv/dt …

so if the force is given as -kv², then that's mdv/dt = -kv²

 

[Michaelbk]

Thank you very much, I appreciate it.