A 25-ft ladder rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 0.18 ft/sec, how fast, in ft/sec, is the top of the ladder sliding down the wall, at the instant when the bottom of the ladder is 20 ft from the wall? Answer with 2 decimal places. Type your answer in the space below. If your answer is a number less than 1, place a leading "0" before the decimal point (ex: 0.35).

Question

arianna1453 · Answer

@idku @Compassionate @TheSmartOne @dan815

freckles · Answer

draw a pic first|dw:1449002757681:dw|...

freckles · Answer

|dw:1449002800063:dw|

arianna1453 · Answer

Right, okay i did that already (:

freckles · Answer

|dw:1449002819798:dw|

freckles · Answer

you can relate w,g, and 25ft using an equation
a famous equation when you talk about right triangles

arianna1453 · Answer

a^2+b^2=c^2

freckles · Answer

yes pythagorean theorem 
w^2+g^2=25^2

freckles · Answer

A 25-ft ladder rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 0.18 ft/sec, how fast, in ft/sec, is the top of the ladder sliding down the wall, at the instant when the bottom of the ladder is 20 ft from the wall? 

let's look at what we are given 
we are giving g' is .18 ft/sec
we are given that we want to find w' when g=20 ft

freckles · Answer

so we could go ahead and find w at this instance g=20 ft

freckles · Answer

but eventually we will also need to differentiate w^2+g^2=25^2 with respect to time

arianna1453 · Answer

This is the part where i get confused.

freckles · Answer

which part finding w when g=20
or finding w'?

freckles · Answer

w' also knows as dw/dt
and
g' also knows as dg/dt

freckles · Answer

just in case you prefer the other notation

arianna1453 · Answer

Well w =15 or -15 right?

freckles · Answer

well distances are positive so w=15 ft

freckles · Answer

ok now we need to differentiate w^2+g^2=25^2 w.r.t time

freckles · Answer

use chain rule and power rule to differentiate w^2 and g^2

freckles · Answer

and to differentiate a constant you get 0
so (25^2)'=0

freckles · Answer

$$(w^2+g^2)'=0 \ (w^2)'+(g^2)'=0$$

freckles · Answer

do you know power rule and chain rule?

arianna1453 · Answer

yes. i do

freckles · Answer

so (w^2)'=?

freckles · Answer

example:
$$\frac{d}{dt}(f(t))^n=n (f(t))^{n-1} \cdot f'(t)$$

arianna1453 · Answer

2w + 2g?

freckles · Answer

well you forgot about the chain rule part

freckles · Answer

w is a function of t 
and g is a function of t
and you are differentiate w.r.t. t

arianna1453 · Answer

2w dw/dt for that? Chain rule still confused me a littel

freckles · Answer

$$2w w'+2g g'=0$$

yes

freckles · Answer

well wouldn't you find the deriavitve of (3x+5)^2
by doing 2(3x+5)^(2-1) *(3)

freckles · Answer

you still have to differentiate the function inside the power

arianna1453 · Answer

Yeah okay.!

freckles · Answer

then plug in your values for w and g and g'
and solve for w'

arianna1453 · Answer

so, so far, 2(15)w' +2(20)g'
 Ugh. Sorry the prime stuff always messes me up.

freckles · Answer

the prime parts are the rates

arianna1453 · Answer

the 0.18 right?

freckles · Answer

|dw:1449004171031:dw|
the bottom of the ladder slides away from the wall at a rate of 0.18 ft/sec

this part is taking about what is going on with g 
g being the distance from the bottom of the ladder to the wall
so g'=.18ft/ sec since that distance is growing  not shrinking
if shrinking we would have said g'=-.18ft/sec