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.
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I should be fine to solve the linear ODE, I just don't know where to start with contructing one.
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hmm i dunno, this one is too "physics"y for me lol
haha, who else on here does calculus?
Hmm I dunno. There are a bunch of smarty pants online right now though :O
Zarkon, Satellite, King George ...
@satellite73, @UnkleRhaukus ?
these guys probably get so many tags that they don't even bother.. lol... the joys of a 99 smartscore.
oh goody @hartnn came online :)
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 ...
v=velocity function ..
haha. Well that is a good start, I don't have any idea either of how to incorporate mg
Fnet = mg - v/5
if the question meant that 'both' downward and upward forces together are 1/5th of speed, then
m dv/dt -mg = v/5 ...
m*dv/dt = mg-v/5 ???
i am still unsure..
no I think just the drag is v/5
hmm, I guess I will just go with one and see what I get.. :)