Non-Linear Golf Club Angles: Regression Analysis and Estimations

[alyssa]

Non-Linear Functions


Introduction: When a golfer hits a golf ball squarely at the bottom of the swing, with the shaft perpendicular to the ground, the ball is propelled into the air in a direction perpendicular to the face of the club [see the diagram below]. The different club angles produce different initial horizontal speeds and different maximum horizontal distances reached along the ground. Various pieces of electronic equipment were used to obtain the data for the various club angles. The information is reproduced in the following chart.


Tasks:


1. Use an appropriate method of regression to find a formula for a relationship between club angle and initial speed. Express the numbers in the formula to 3 decimal places.


2. Draw the scatter plot as well as the curve of the relationship found in question 1 on the graph paper provided.


3. Use your formula to estimate the initial speed when the club angle is 25 degrees.


4. What would the club angle be if the initial speed were 45 metres per second?


5. Use an appropriate method of regression to find a formula for a relationship between club angle and the maximum horizontal distance reached. Express the numbers in the formula to 3 decimal places.


6. Draw the scatter plot as well as the curve of the relation found in question 5 on the graph paper provided


7. Use your formula to estimate the maximum horizontal distance reached when the club angle is 45 degrees.


8. What would the club angle be if the maximum horizontal distance reached were 120 metres?


9. On the third piece of graph paper extend the graph make in question 6 into the second quadrant.


http://i2.photobucket.com/albums/y9/clubenvy/one.jpg


http://i2.photobucket.com/albums/y9/clubenvy/two.jpg


http://i2.photobucket.com/albums/y9/clubenvy/three.jpg


http://i2.photobucket.com/albums/y9/clubenvy/four.jpg

 

[xanthym]

You can use following Web Site to enter your data and experiment with (and graph) polynomial regressions of various degrees. Select the polynomial regression of least degree that approx fits your data. The "best-fit curve" equation is printed out beneath the graph for use with your question items.
http://www.arachnoid.com/polysolve
(Scroll down page for the interactive program. Allow time for program to start.)


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[alyssa]

unfortunately my computer is not downloading the interactive program correctly .

 

[Shockwave]

What, one place wasn't enough? http://www.mathgoodies.com/forums/topic.asp?TOPIC_ID=21576

 

[xanthym]

unfortunately my computer is not downloading the interactive program correctly .

Here's another Web Site for polynomial regression that might work on your computer. Give program time to start and read instructions left side of page.
http://www.shodor.org/chemviz/tools/regressionjava/


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