1. ## related rates problem

A leadder 25ft long is leaning against the wall of a hour. The base of the ladder is pulled away from the wall at a rate of 2ft/sec

(my picture isnt to scal for some reason)

|\
r | \ 25ft
| \
|----\
7ft

a.) How fast is the top of the ladder moving down the wall when it's base is 7ft from the wall?

i understand i can do pythag. theorom to get side of r which is 24 but im unsure of how to find dr/dt? do i still use pythag. theorom to solve for dr/dt? if so im unsure how to do it....any explanation would be greatfull!

2. Originally Posted by maybnxtseasn
A leadder 25ft long is leaning against the wall of a hour. The base of the ladder is pulled away from the wall at a rate of 2ft/sec

(my picture isnt to scal for some reason)

|\
r | \ 25ft
| \
|----\
7ft

a.) How fast is the top of the ladder moving down the wall when it's base is 7ft from the wall?

i understand i can do pythag. theorom to get side of r which is 24 but im unsure of how to find dr/dt? do i still use pythag. theorom to solve for dr/dt? if so im unsure how to do it....any explanation would be greatfull!
Think of the side r as a function of x.

$r^2=(25)^2-x^2$

$2r\frac{dr}{dt}=2x\frac{dx}{dt}$

$\frac{dr}{dt}=\frac{x}{r}\frac{dx}{dt}$