Quantitative Skills > Teaching Resources > Activities > Vectors and slope stability

Vectors and slope stability

Eric Baer (based on material from Baer and Whittington (2006))

Geology Program, Highline Community College, Des Moines, WA
Author Profile

This activity was selected for the On the Cutting Edge Exemplary Teaching Collection

Resources in this top level collection a) must have scored Exemplary or Very Good in all five review categories, and must also rate as “Exemplary” in at least three of the five categories. The five categories included in the peer review process are

  • Scientific Accuracy
  • Alignment of Learning Goals, Activities, and Assessments
  • Pedagogic Effectiveness
  • Robustness (usability and dependability of all components)
  • Completeness of the ActivitySheet web page

For more information about the peer review process itself, please see http://serc.carleton.edu/NAGTWorkshops/review.html.

This page first made public: Jul 26, 2006


This homework or in-class activity is designed to teach students with little or no experience with vectors, free-body diagrams, or the like to apply vectors to slope stability problems.

Students first learn the basic properties of vectors, vector addition, resolving forces, etc. They then apply these techniques to establish in a simplified way how geologists can determine if a slope is stable, how much loading a slope can withstand to become unstable, and other principles of slope stability determination.

This activity is used in an introductory geohazards course with no pre-requisites. It can be completed in one to two hours.

Learning Goals

At the end of this exercise students should be able to:

Context for Use

This is used as homework in an introductory geohazards course. I use it after introducing vector notation and using it to help generate a list of factors which impact the stability of a slope. I like it because it allows what is usually a topic that is treated qualitatively (forces in mass movement) to be treated more quantitatively.
It can be done in an evening but often students require some additional assistance from a tutor or someone who has seen vectors before.

Teaching Notes and Tips

Students will need protractors, rulers, and perhaps a calculator (if they want to use trigonometry to solve the last question.)
Note that pounds are used as the force units so that students do not need to convert between units of weight and force, as would have to be done if the metric system was used. I found this reduced student errors.

Teaching Materials

Vectors and Slope Stability (Microsoft Word 56kB Feb11 06)

This assignment has two parts. The first is a general introduction to vectors, graphical manipulation of vectors and vector addition. The second part of the homework asks students to look at vector diagrams to see if a house is stable on slopes of differing angles. A final question asks students to find the maximum weight for a house on a given slope with known friction.


I grade the completed work and place at least one question on a quiz similar to these problems. Another way of assessing is to ask the question why a house on a steep slope is more likely to slide than the same house on a gentle slope.

Contact the Author

Please contact the author with questions or suggestions ebaer@highline.edu 206-878-3710 x 3513

Controlled Vocabulary Terms

Subject: Environmental Science:Natural Hazards:Mass Wasting, Geoscience:Geology
Resource Type: Activities:Problem Set, Classroom Activity, Lab Activity
Inquiry Level: Step-By-Step Instruction
Special Interest: Quantitative, 2YC:Geo2YC, Geo2YC- OLD DO NOT USE, Hazards
Grade Level: College Lower (13-14)
Quantitative Skills: Vectors and Matrices, Problem Solving
Ready for Use: Ready to Use:Tested, Ready to Use
Quantitative Skills Activity Type: Classroom Activity, Problem Set, Lab Activity
Science Background Required: Broadly accessible
Topics: Human Dimensions/Resources, Earth surface
Solid Earth Processes: Weathering/Erosion
Theme: Teach the Earth:Course Topics:Environmental Science, Teach the Earth:Incorporating Societal Issues:Hazards, Teach the Earth:Teaching Environments:Two-Year Colleges

See more Activities »