Potential Scenario

2006-G_Ashline-J_Ellis-Monaghan-How high-fast-long-Modeling water rocket flight with calculus

Author(s): George Ashline1, Joanna Ellis-Monaghan1


Keywords: calculus Flight projectile water rocket

81 total view(s), 35 download(s)


Resource Image We describe an easy and fun project using water rockets to demonstrate applications of single variable calculus concepts.


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Article Context

Resource Type
Differential Equation Type
Qualitative Analysis
Application Area
Course Level
Lesson Length


Ashline, George and Joanna Ellis-Monaghan. 2006. How high? How fast? How long? Modeling water rocket flight with calculus. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 16(2): 121-137.

See . Accessed 27 March 2023.

Article Abstrct: We describe  an easy  and  fun  project  using  water rockets to demonstrate applications of single variable calculus concepts. We provide procedures  and a supplies list for  launching and  videotaping a water rocket flight to provide the experimental data. Because of factors such as fuel expulsion and wind effects, the water rocket does not follow the parabolic  model  of  a textbook  projectile , so instead we develop a one-variable height vs. time polynomial model by in­terpolating observed data points. We then analyze this model using methods suitable to a first semester calculus course. We include a list of questions and partial  solutions for our project  in which  students use calculus techniques to find quantities not apparent from direct observation. We also include a list of websites and other resources to complement  and  extend this project.

While this piece specifically does NOT use differential equations it is about how one could collect data to use in a differential equation model for projectile motion. Moreover, there are several excellent references.


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Author(s): George Ashline1, Joanna Ellis-Monaghan1




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