Question

The top of a ladder slides down a vertical wall at a rate of 5/24 m/s. At the moment when the bottom of the ladder is 5 m from the wall, it slides away from the wall at a rate of 1/2 m/s. How long is the ladder?

a) State what you're given and what you find.
Draw and label the picture of the problem. Be sure to define all variables.

b) Set up your related rate equation and solve.

c) Write your answer in a complete sentence with the appropriate units

Answer 1

make a triangle and apply Pythagoras rule:
\[x ^{2}+y ^{2}=h ^{2}\]
here h represents the length of the ladder

Answer 2

The first posting had an error; the revised solution is attached.
Mathematica 9 was used for the calculations.

Answer 3

derive the whole equation knowing that "h" is constant, then:
\[2x.\frac{ dx }{dt } + 2y.\frac{ dy }{ dt }=0\]

replace to get missing value "y".
The last step would again use main equation of Pythagoras to find h.
I hope this is helpful :)

Answer 4

what I provided is much easier than your mathematica's solution :)

Answer 5

@mlearning24

Did your easier solution also determine the ladder length to be 13 m ?

Answer 6

you should find out.. can't you !!

Answer 7

thank you so much!!!!!!

Answer 8

Your welcome.