Question

The base of a ten-foot ladder is being pushed away from the wall it is leaning against .
If the base is moving at a rate of 2 feet per minute find the rate at which the top of the
ladder is moving when the lower end of the ladder is 3 feet from the wall describe the
significance of the sign of your results . discs s whether or not this sign depends on which
side of the wall the ladder is leaning .

Answer 1

did you draw a picture?

Answer 2

okay let me work it out

Answer 3

no, h is not changing with time. (h is fixed at 10 ft., the length of the ladder).

Answer 4

2x*dx/dt=100

Answer 5

dh/dt = 0

Answer 6

\[x^2+y^2=h^2 \Rightarrow 2x \frac{ dx }{ dt }+2y \frac{ dy }{ dt }=0\]

Answer 7

they're asking for dy/dt

Answer 8

oh, so constant is 10 and the derivative of it is 0

Answer 9

how come the y isn't a constant?

Answer 10

look at the triangle... as x increases, y has to decrease because h stays constant.

Answer 11

oh... will y be sqrt 91 then?

Answer 12

yes... y = sqrt(100-9) = sqrt(91)

Answer 13

its a negative sign because the y is shrinking right?

Answer 14

yep

Answer 15

if the base is moving away from the wall then x is always increasing and subsequently, y will always be decreasing.

Answer 16

if the base moves towards the wall then x will be decreasing and in that case, y would be increasing.

Answer 17

oh~~~ I get it now xD

Answer 18

just get a 10' ladder and try the experiment... maybe use a strobe or slow motion video.

Answer 19

Alright! Thanks a lot!

Answer 20

you're welcome!