A "retarded" mechanics question (1 Viewer)

[hectic18]

Sorry about the title lol, but here goes..

This question is in new senior mathematics, fitzpatrick 4U (page 165, q6), i just don't seem to get any of these resisted motion q's.

"A particle falls from rest in a medium. If the retardation due to resistance in the medium varies as the square of the velocity, find the distance fallen as a function of the velocity. What is the terminal velocity? Find the distance fallen when half the terminal velocity is reached."

I think it's something wrong with my equation? I've got mg - kv² = mv(dv/dx)

Cheers.

 

[malady]

Nothing wrong with the equation... Its your integration skill that's lacking:
x=int(v/(g-kv^2))dv etc...

 

[hectic18]

Its your integration skill that's lacking:
x=int(v/(g-kv^2))dv etc...

yeah that sounds about right lol xD. btw thanks for replying so early in the day

I managed to obtain the answer with your equation, but how did you manage to obtain that eqn in the first place? my working comes out like this

mg - kv² = mv(dv/dx)

dx = mvdv/(mg-kv²)

x = m int[v/(mg-kv²)dv]

and yeah, ends up wrong, i still can't find the error in my shifty integration >.<

 

[ianc]

okay you stuffed up right at the beginning where you're resolving forces: you forgot to make the retarding force mkv² - you simply left it as a value for acceleration

anyway, here's the whole solution:

 

[ianc]

i had another look at the thread and i realised i hadn't seen the second part of the question, so here goes:

These resisted motion questions are basically all about algebra - once you've got the initial formulas you've just got to work accurately

 

[hectic18]

Yeah, i better remember to include the m as part of the resistance lol xD. wow great explanation there ianc Thanks for the help guys