Mechanics solutions please!! (1 Viewer)

[Romany5]

Ok, I'm doing mechanics, and I'm using the Fitzpatrick textbook (coz it is way easier!!) and I was wondering if anyone could help with this question:
A particle falls from rest from 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 have found the formula for x : x = 1/2k ln(g/g-kv^2) and I have found the terminal velocity : v = square root of g/k But I dunno how to found the distance when half the terminal velocity is reached.
Please help?

 

[evanstroeve]

Looks like you've done all the hard work already.
Half the terminal velocity:
v^2 = g/4k
Substitute v^2 into x as a function of v:
x = (-1/2k)log((g-g/4)/g)
x = (1/2k)log(4/3)

I think that's it. Hopefully someone who knows LaTeX can make it clearer.

 

[Romany5]

Thank you very much!!!! I must say, Mechanics is a bitch.