Hello! I am Tweety. Today, I get the bird…. Hector Created by Daniel Cromer .

Hello! I am Tweety.

Today, I get the bird….

Hector

Created by Daniel Cromerhttp://www.danielcromer.com

I will wait until Tweety is up on his bird house. Then, I’ll take a ladder and snatch him!

Hector, I am going to my birdhouse. Watch out for the

cat.

Yes boss.

Tweety is resting in a bird house, 24 feet off the ground.

Using a 26 foot ladder, leaned against the pole holding the bird house, Sylvester tries to steal the small yellow bird.

Tweety’s bodyguard, Hector the dog, starts pulling the base of the ladder away from the pole at a rate of 2 ft/s.

How fast is the ladder falling when it is 10 ft off

the ground?

26 ft

24 ft

Not so fast!!!

!!

How fast is the ladder falling (dy/dt) when it is 10 ft off the ground (y)?

26 fty

x

Known Values:

ft/s2dt

dx

ft10y

ft26L

LS

olve

for

:

dt

dy

Equation:

222 L yx

Solving for related rates:

1. Prepare Equation

2. Substitute Values

26 fty

x

L

Equation:

222 L yx

Solving for related rates requires the derivative of the equation with respect

to time.dt

dy

Sol

ve f

or:

dt

dy

ydtdxx

dt

dy

How fast is the ladder falling (dy/dt) when it is 10 ft off the ground (y)?

26 fty

x

Known Values:

ft/s2dt

dx

ft10y

ft26L

LS

olve

for

:

dt

dy

Equation:

222 L yx

ydtdxx

dt

dy

Solving for related rates:

1. Prepare Equation

2. Substitute Values

Known Values:

ft/s2dt

dx

ft10y

ft26L

Equation:

ydtdxx

dt

dy

dt

dy

Known Values:

ft/s2dt

dx

ft10y

ft26L

Equation:

222 L yx

x ft24x

Known Values:

ft/s2dt

dx

ft10y

ft26L

Equation:

ydtdxx

dt

dy

ft24x

ft10

ft/s)2(x

dt

dy ft/s8.4

dt

dy

4ft2

How fast is the ladder falling (dy/dt) when it is 10 ft off the ground (y)?

26 fty

x

Known Values:

ft/s2dt

dx

ft10y

ft26L

L

Equation:

ydtdxx

dt

dy

Solving for related rates:

1. Prepare Equation

2. Substitute Values

ft/s8.4dt

dy

Tweety is resting in a bird house, 24 feet off the ground.

Using a 26 foot ladder, which Sylvester leans against the pole, holding the bird house, Sylvester tries to steal the small

yellow bird.

Tweety’s bodyguard, Hector the dog, starts pulling the base of the ladder away from the pole at a rate of 2 ft/s.

How fast is the ladder falling when it is 10 ft off

the ground?

ft/s8.4dt

dy

I am so very happy! I have been saved

from the cat!