One end of a rope is fastened to a boat and the other end is wound around a windlass located on a dock at a point 4 meters above the level of the boat. (see picture in the book) If the boat is drifting away from the dock at the rate of 2 meters/min , how fast is the rope unwinding at the instant when the length of the rope is 5 meters . (Let denote the length of rope at time .)
Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
\[y'\] and you know that
\[y^2=4^2+x^2\] and therefore
\[2yy'=2xx'\] you are given that
\[x'=2\]so you can plug in the numbers to get the answers
Not the answer you are looking for? Search for more explanations.
no i think your pic is right
or atleast i drew the same thing
so now that i know x^prime what do i do?
then this should be easy enough. you have
\[x'=2,x=5\] and by pythagoras we find
was x prime in the problem?
when it says it is pulling away at 2ft/sec
so you get
if you label the distance from the boat to the dock as x, then you know x' = 2 because that is what you are told
ok i see
the boat is drifting away from the dock at the rate of 2 meters/min
that tells you x' = 2, if you label that distance as x
you need to call it something because you are trying to find the rate of change of the rope, and you only know the rate of change of the boat. your goal is to find an equation that relates them so you can differntiate and solve for the rate of change that you want, using the rate of change that you know
so the sqrt(41)y^prime = 10 and i just solve for y^prime and thats my answer