Question

A 26 foot long ladder is leaning against a vertical wall. The foot of the ladder is 10 feet away from the base of the wall. The foot of the ladder is being pulled away from the base of the wall at a rate of 4 feet per second. How fast is the top of the ladder sliding down the wall at this instant? (related rates)

Answer 1

related rates problem awesome!

Answer 2

cyter beat me

Answer 3

lol wrong problem

Answer 4

could both answers be correct?

Answer 5

lol there are two different answers
let me see if i made a mistake

Answer 6

You used 4 instead of 10

Answer 7

cyter is right

Answer 8

i used y' for y my bad

Answer 9

cyter wins

Answer 10

we both win because we spent energy working on the problem

Answer 11

lol

Answer 12

in the writing in the purple, isn't the derivative of s^2 2s, not just 2?

Answer 13

yep

Answer 14

the right hand side should have been 2s ds/dt
I knew something was amiss.

Answer 15

since s is a constant (it doesnt change)
s'=0
so 2ss'=0

Answer 16

so it doesnt change the answer

Answer 17

yep it makes no difference but it looks logical

Answer 18

right
and it is best to be logical during to look crazy

Answer 19

than not during*

Answer 20

but what happens to the 2s? does it cancel out? and how does the x (dx/dt) becomes negative?

Answer 21

2ss'=0

Answer 22

the derivative of s^2 is 2ss'
but since s doesnt change s'=0

Answer 23

oo right, sorry

Answer 24

factor out the 2 s and devide both sides by 2
0/2 = 0

Answer 25

cyter did you draw that on the computer? it looks very mechanical like

Answer 26

on some parts

Answer 27

lol looks better than my horrible hand writing

Answer 28

\[\text{2((xdx/dt)+(ydy/dt) = 2sds = 0/dt}\] dividing both sides by 2 we have
\[\text{((xdx/dt)+(ydy/dt) = sds/dt = 0}\] now subtract both sides by (xdx/dt) we get
\[\text{(ydy/dt) = -(xdx/dt)}\] and then divide both sides by y to get dy/dt alone
\[\text{(dy/dt) = -(x/y)dx/dt}\] Then plug and play

Answer 29

yes I used paint which isn't very good

Answer 30

Your handwriting is legible, unlike mine where I have to use a drawing program on my computer

Answer 31

i have a scanner haha

Answer 32

lol

Answer 33

ok i get it now, thank you both of you for your help

Answer 34

glad to help

Answer 35

Using cyter's solution diagram,
\[y=x \text{Tan}[\text{ArcCos}[x/26]] \]
then
\[y=26 \sqrt{1-\frac{x^2}{676}} \]
The total derivative of the above is:
\[\text{Dt}[y]==-\frac{x \text{Dt}[x]}{26 \sqrt{1-\frac{x^2}{676}}} \]
Replace x with 10 and Dt[x] with 4 and simplify,
\[\text{Dt}[y]==-\frac{5}{3} \]
I hope there are no errors. First DE solved in years.