A certain object of mass 3kg is dropped into a liquid and, as it falls through it, it is subject to the downward force of gravity and the upward force of drag, which is given by one fifth of its speed. Express this statement as a differential equation and solve such equation to identify the velocity function for the object.

Question

baldymcgee6 · Answer

@zepdrix :)

baldymcgee6 · Answer

I should be fine to solve the linear ODE, I just don't know where to start with contructing one.

zepdrix · Answer

hmm :(

zepdrix · Answer

hmm i dunno, this one is too "physics"y for me lol

baldymcgee6 · Answer

haha, who else on here does calculus?

zepdrix · Answer

Hmm I dunno. There are a bunch of smarty pants online right now though :O
Zarkon, Satellite, King George ...

baldymcgee6 · Answer

@satellite73, @UnkleRhaukus ?

baldymcgee6 · Answer

these guys probably get so many tags that they don't even bother.. lol... the joys of a 99 smartscore.

baldymcgee6 · Answer

oh goody @hartnn came online :)

hartnn · Answer

seen such question for the first time, but still i'll give it a try...
downward force of gravity  =ma = mg (acceleration is due to gravity, so a=g)
upward force of drag = ma = m dv/dt (v=velocity)
given that mdv/dt = 1/5th of its speed = v/5 

mdv/dt = v/5 in itself is a DE, donno how to incorporate mg ...

hartnn · Answer

v=velocity function ..

baldymcgee6 · Answer

haha. Well that is a good start, I don't have any idea either of how to incorporate mg

baldymcgee6 · Answer

Fnet = mg - v/5

hartnn · Answer

if the question meant that 'both' downward and upward forces together are 1/5th of speed, then
m dv/dt -mg = v/5 ...

baldymcgee6 · Answer

m*dv/dt = mg-v/5 ???

hartnn · Answer

or that^ 
i am still unsure..

baldymcgee6 · Answer

no I think just the drag is v/5

baldymcgee6 · Answer

hmm, I guess I will just go with one and see what I get.. :) 
thanks guys!