Question

A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second. (Do not use mixed numbers. Round your answers to three decimal places.)
(a) How fast is the top of the ladder moving down the wall when the base is given below?
15 feet away from the wall
_____ ft/sec

20 feet away from the wall
_____ ft/sec

24 feet away from the wall
_____ ft/sec

...?

Answer 1

last one. i can do the first part. put x = distance from top of ladder to the floor, y = distance from base of ladder to the wall (draw a picture) then pythagoras sez

x2+y2=25

calculus says

2xx′+2yy′=0

and you are told that

y′=2

so you know

2xx′+4y=0

or

x′=−2yx