Desperately need help

[Sebastian]

I have a differential equations problem that I thought someone here may be able to help with. So here goes:
In the motion of an object through a certain medium (air at certain pressures is an example), the medium furnishes a resisting force proportional to the square of the velocity of the moving object. Suppose a body falls due to the action of gravity, through the medium. Let t represent time, and v represent velocity, positive downward. Let g be the usual constant acceleration of gravity, and let w be the weight of the body. Use newton's law, for equals mass times acceleration, to conclude that the differential equation of motion is
(W/g)dv/dt=w-kv^2
where kv^2 is the magnitude of the resisting force furnished by the medium.

If no one can help, do you know of any places that my be able to? This assignment is due tomorrow. **** I hate doing this, but i can't for the life of me figure this god damn thing out.

 

[Tyguy]

your in luck....

the answer is 7

 

[xcellerate]

if I didn't have math homework and a C++ project due I would help you out...maybe if I can get it all done soon enough I'll give it a whirl...

 

[Sebastian]

Forget it, Tyguy already provided the answer. that's all I need. But seriously, I would greatly appreciate it xccelerate.

 

[63]

No, the answer actually is 7.

 

[mindless_moder]

its simple the net force on the object = m * a . therefore
w(the force due to gravity) - (kv^2) (the force due to resitance) will give you the netforce which equals w/g(the mass since weight is just mass*9.8) multiplied by a (dv/dt represents the change in velocity over time which is the same as a) .
edit:the answer is 7 :S ?

 

[Sebastian]

gracias mi amigo. It feels good to finally know.

 

[Sebastian]

Sorry for the double post, but I ran into some troubles.

Default
I understand the first part, but this second and third parts are getting me:
b) Solve the differential equation of part A, with the initial conditions that v=v0 when t=0. Introduce the constant a^2=w/k to simpilfy the formulas.

c) There are mediums that resist motion through them with a force proportional to the first power of the velocity. For such a medium, state and solve problems analogous to parts A) and B), except that for convenience a constant b=w/k may be introduced to replace the a62 of exercise 19. Show that b has the dimensions of a velocity.

 

[Raziaar]

if I didn't have math homework and a C++ project due I would help you out...maybe if I can get it all done soon enough I'll give it a whirl...

You should ditch C++ and take up C#. We'll learn it together. I need a buddy to motivate and help me through. heh.