calculusssssssss

Question

A 14-foot ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate of 2 ft/s., how fast will the end be moving away from the wall when the top is 6 ft. above the ground.

Answer 1

hypotenuse squared= sum of squares of the other two sides

h^2 =a^2 + b^2

take derivatives with respect to time

2hh' = 2aa' + 2bb'

h'=dh/dt, a' = da/dt, b'= db/dt

divide by 2

hh' = aa' + bb'

where a =6, a' =2, h=14, h'=0 b =sqr(14^2-6^2) = about 12.65 = 4sqr10

14(0) = 6(2) +4sq10(b')

b' = -12/4sqr10 = -3/sqr10 = about -0.949 ft/s

b'<0 to indicate its distance is getting further away from the wall

this is a "related rates" problem. You should find a few pages on that topic, usually under a bigger section labeled "derivatives." in your textbook. check the index to find them.