1. Tweety, Sylvester, Hector, and the Ladder
A Mathematical Adventure...
Created by Daniel Cromer
Today, I get the bird….
Hello! I am Tweety.
Hector

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

3. Hector, I am going to my birdhouse. Watch out for the cat.
Yes boss.

4. ! 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?
Not so fast!!!
26 ft
24 ft

5. Solving for related rates:
How fast is the ladder falling (dy/dt) when it is 10 ft off the ground (y)?
26 ft y L
Known Values: x
Equation:
Solving for related rates:
Prepare Equation
Substitute Values
Solve for:

6. 26 ft y L x
Equation:
Solving for related rates requires the derivative of the equation with respect to time.
Solve for:

7. Solving for related rates:
How fast is the ladder falling (dy/dt) when it is 10 ft off the ground (y)?
26 ft y L
Known Values: x
Equation:
Solving for related rates:
Prepare Equation
Substitute Values
Solve for:

8. Known Values:
Equation:

9. Known Values:
Equation:

10. Known Values:
Equation:

11. Solving for related rates:
How fast is the ladder falling (dy/dt) when it is 10 ft off the ground (y)?
26 ft y L
Known Values: x
Equation:
Solving for related rates:
Prepare Equation
Substitute Values

12. 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?

13. And Tweety lived happily ever after...
I am so very happy! I have been saved from the cat!