A ladder 13 meters long rests on a horizontal grounds and leans against a vertical wall. The foot of the ladder is pulled away from the wall a rate of 0.6 m/sec. How fast is the top sliding down the wall when the foot of the ladder is 5 m from the wall?

Question

anonymous · Answer

Alright, first write the height of the ladder as a function of the distance of the base from the wall.

anonymous · Answer

Know how to do that?

anonymous · Answer

pythagorean

anonymous · Answer

pythagoras all the way.  height is h, base is b so you have 
$$h^2+b^2=13^2$$ taking derivatives wrt time you get 
$$2hh'+2bb'=0$$ you are told that 
$$b'=.6$$ so solve for 
$$h'$$

anonymous · Answer

ok

anonymous · Answer

h being height and b being base, or the distance from the wall.

anonymous · Answer

$$h'=-\frac{bb'}{h}$$ and you know 
$$b'=.6, b=5$$ and since 
$$b=5$$ you know by pythagoras again that 
$$h=12$$ plug in the numbers and get your answer

anonymous · Answer

for some reason math teachers  love these ladder problems.  those and the oil spill ones and the plane flying overhead and the one with the lamp and the shadow.  familiarize yourself with them if there is going to be a test.

anonymous · Answer

oh jeeze. no dh/dt or anything. haha thanks so much

anonymous · Answer

well if you are dying to write more feel free to write 
$$2b\frac{db}{dt}$$ etc

anonymous · Answer

haha. I'm just kidding. Thank you so much!