Question

Fun and Challenging Word Problem!

Answer 1

Lots of fun :)

Answer 2

https://docs.google.com/document/d/1MCidnRDmwE2RxXkZio0ZbCfYEuAqOZxajf6KW7Yrpyo/edit?usp=drive_web

Answer 3

yup thats fun -_-

Answer 4

LOL very fun

Answer 5

Where are you stuck? I see no Bournoulli here, just a trig substitution

Answer 6

after the sub you get
dz/dx=k*sqrt(1+z^2)
separate the variables to get
dz/sqrt(1+z^2)=kdx
integrate both sides and you'll get an inverse hyperbolic trig function on the left, which you can take the inverse of to put on the right, then sub dy/dx for z, separate and integrate again. And for the love of heck, don't drop any constants along the way, you'll need to apply those boundary conditions at the end of you want the right answer!

Answer 7

arcsinh(z)=kx+c
can i divide by arcsinh to get:
z=sinh(kx+c)
is that legal?

Answer 8

also can someone please tell me where archsinhz comes from? how would i show my work from
dz/sqrt(1+z^2)=kdx to
arcsinh(z)=kx+c