What Factors Influence the Equation for a Bouncing Ball's Range?

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To derive a general equation for the range of a bouncing ball, factors such as the coefficient of restitution, initial drop height, and the angle of impact should be considered. The discussion emphasizes the need for a theoretical approach rather than relying solely on software tools like Excel for curve fitting. Suggestions include analyzing the relationship between drop height and bounce distance through experimental data. The user seeks guidance on formulating a mathematical model based on their collected data. Overall, the focus is on creating an accurate equation that reflects the physics of bouncing balls.
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Homework Statement


I was wondering if someone could aid me in finding a general equation for this data. In my physics lab we had to drop a small steel ball over a steel bounce plate and record the range from the base of the bounce plate that it went. This was done 18 times from several heights and then averaged. I know I need to take into account the coefficient of restitution, what else should I take account of and do you have any suggestions about how to get a good equation going through this data.
Any suggestions? Thanks

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The Attempt at a Solution


I've included a graph of the data below
 

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If I recall correctly, MS Excel does have a "fit polynomial to curve" function, after you sketch a graph of the data you have. You can even choose the value of the highest order polynomial you want to approximate your curve with.
 
I have to determine this using theory not using excel. Can someone please help me?
 
Here is a better description of the problem
 

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