Help! I've tried for 10+ hours

[amph1bius]

I've tried question #1 on here:
http://www.pa.uky.edu/~cvj/PHY404G/phy404g98_test1/phy404g98_test1.html

for the past 10 hours, i have achieved getting something relatively close, but i cannot do the algebra to prove t=cosh^(-1) etc etc...

has anyone done this problem in the past, i know nitrus has a similar one, and i have talked to him, but it was of no use.

please help me, it is very appreciated.

thanks,

[krab]

There is a time integral and a distance integral. Did you get those? They are each of the form of the 2 integrals given as hints. Combine and you get

sqrt(k g sin(theta)) t =

(1/2) ln((1+sqrt(Q))/(1-sqrt(Q)))

where

Q = 1 - exp(-2 k d)

The big thing with the ln in it is actually equal to

cosh^-1(exp(kd)),

though it is not obvious. So you are done.