Question: Find parametric equations that model the problem situation. Use the GeoGebra tool to graph the parametric equations. Find all possible values for t that represent
- Find parametric equations that model the problem situation.
- Use the GeoGebra tool to graph the parametric equations.
- Find all possible values for t that represent the situation.
- State the parametric equations.
- State the domain and range for each parametric equation.
- Plot the minimum and maximum heights of the dart.
- Plot the minimum and maximum horizontal positions of the dart.
- Find the time at which the dart reaches the maximum height.
- Save your GeoGebra work as a .pdf file for submission.
Part II: Based on your work in Part I, discuss the following:
- Discuss why this situation can be modeled using parametric equations.
- Discuss how you determined all possible values for t that represent the situation.
- Discuss what the domain and range of the parametric equations mean in the context of this problem.
- What do maximum and minimum values of the parametric equations represent in this context?
- Discuss how your answers to Part I would be affected if:
- The initial velocity is increased.
- The angle of elevation is decreased.
- Provide at least two other real-world situations that can be modeled using parametric functions and respond to the following:
- What common characteristics do the real-world scenarios you chose share?
- What did you look for in the way that the real-world scenario can be modeled?
- How can you verify that the real-world scenarios you chose can be modeled by parametric functions?
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