Parametric Equations: A Hole in One!
- Robert Reed
An Introduction to the Activity
Common Core State Standards addressed in this activity
Task 1: Exploring
Describe how the trajectory of the ball changed as you manipulated the angle and velocity of the hit.
Task 2: Experimenting
Record your three answers below in the format [Angle, Velocity] and separate each answer with a line break.
Task 3: Approximating a Solution
What velocity resulted in a direct shot into the hole when the hit angle was 30?
Task 4: Finding and Using a Model
In order to write our model we'll need to identify the important information from the passage above. In the space below, record any important information that you think we may need in solving this problem.
Writing a Model
Use the information above to come up with a set of parametric equations that will model the path of the ball. Feeling stuck? Take a look at the video below for a quick refresher on how to do this. Note that the video provides a generalized solution to this problem, but it will still be up to you to apply it to this particular scenario.
Modeling Projectile Motion: Review
The exact location of the hole is (33.435, 0). Use your model from the previous question to determine if the shot was in fact a direct shot into the hole. Explain how you determined your answer and provide any supporting evidence used in your explanation.
Test your results!
Task 5: Review and Extensions
The golfer hits the ball at an angle of 71.652 with an initial velocity of 40 f/s and sinks a direct shot into the hole. Given that the ball starts at a height of 12 feet and the hole is located at (33.435, 0), how long does it take for the ball to reach the hole? Feeling stuck? Scroll down for hints and help with this problem.
This time the golfer hits the ball with an initial velocity of 72 f/s at an angle of 84. What is the maximum height above the hole that the ball reaches, and how long does it take to get to that point? Feeling stuck? Scroll down for hints and help with this problem.
In this round the golfer hits the ball at an angle of 87. Determine the velocity of the hit that would result in a direct shot into the hole. Feeling stuck? Scroll down for hints and help with this problem.
A more challenging hole is located at the coordinates (100, 0). If the ball is hit with an initial velocity of 95 f/s, determine the two angles that would result in a direct shot into the hole. Feeling stuck? Scroll down for hints and help with this problem.
Hints and Videos for Task 5
Hints for Question 1
Solution for Question 1
Hints for Question 2
Solution for Question 2
Hints for Question 3
Solution for Question 3
Hints for Question 4
Solutuion for Question 4
Use the space below to summarize your thoughts on the activity. Reflect on the use of mathematical models and parametric equations and their application to solving real-world problems.