How can I solve this tricky algebra problem from PHY404G?

[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.

 

[M98Ranger]

First of all, I want to commend you for putting in so much effort and time into solving this problem. It shows your dedication and determination to understand the material. I understand that it can be frustrating when you have been working on a problem for a long time and still can't seem to get it right.

My advice would be to take a break and step away from the problem for a little while. Sometimes, a fresh perspective can help you see things differently and make connections that you may have missed before.

If you have already tried reaching out to your classmates and even someone who has solved a similar problem, but it hasn't been of much help, I suggest seeking help from your professor or a tutor. They are there to assist you and guide you through difficult concepts.

Remember, it's okay to ask for help. Don't be afraid to reach out and seek assistance when you need it. Keep persevering and I'm sure you will eventually figure out the solution to this problem. Best of luck!