# Related Rates Walk Through

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```					Related Rates Walkthrough                                         Name _________________________

Period ________________________

Directions: Read each problem below and complete the subsequent numbered task. Show significant
work for each step. Use the applet to verify the solution.

A 10 meter ladder is leaning against
the vertical wall. If the base of the
from the house at a rate of 0.6 meters
per second, how fast is the top of the
ladder sliding down that wall at the
instant when the base of the ladder is
4 meters from the wall?

[1] Identify the geometric shape and determine variables.

Shape ________________________           Variables _________________________

[2] Will the length of the ladder change as it slides down the wall? ____________

[3] Write the variables rates of change as derivatives with respect to time. Note which ones are known
and which one is needed to be found.

*4+ Determine the relationship between the variables (hence “related rate”). Write the proper
geometric formula here.

[5] Differentiate the geometric formula implicitly with respect to time.

[6] Plug in known values and solve.
Teacher Resources

Standards:    Calculus AB II. Derivatives, Application of Derivatives: Modeling rates of change,
including related rates problems.

Objectives:    Students will setup and solve related rates problems

 Students will apply prerequisite knowledge of geometry to related rates

 Students will apply previously learned implicit differentiation

Materials:     Computer Lab

 Accessibility to GeoGebra through installed software or Internet (webstart)

 Ladder Sliding Down Wall interactive Geogebra file

 Related Rates Walkthrough Worksheet

Notes:         Confirm that the file works in the lab on student computer before class

 Distribute worksheets and individually guide students as needed

 Global questions:

 Why is the answer for dwall negative?

 What additional calculation needs to be made to solve for dwall?

(Pythagorean Theorem is needed to solve for wall)

Extension:    Give each student a different set of values to solve for dwall. Students will be
able to verify each answer with GeoGebra.

```
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