Introduction

In this experiment, a motion detector was used to collect distance, velocity, and acceleration data for different types of balls being thrown straight up in the air. Like a juggler who tosses a ball straight upward, each ball slows down on it’s path to maximum height, then begins to speed up on it’s way down. The concept is that there is a definite mathematical pattern to the changes in velocity, which will be reinforced by experimentation.

Analysis

**(2) How closely does the coefficient of the x ^{2} term in the curve fit of the d/t graph compare to ½ g?
**The coefficient of the x

^{2}term in the graph has a magnitude of 4.663, whereas ½ g has a magnitude of about 4.91, therefore the coefficient differs by 0.247 m/s

^{2}.

**(3) How closely does the coefficient of the x term compare to the accepted value for g? (v/t graph)
**The coefficient of the x term in the v/t graph has a magnitude of 9.356, whereas gravity has a magnitude of 9.81, therefore the coefficient differs from the accepted value by 0.454 m/s

^{2}.

**(4) How closely does the mean acceleration value compare to the values of g found in Steps 2 and 3?
**The value for mean acceleration has magnitude of 9.550, differing from the g value in

**Step (2)**by0.230 m/s

^{2}, and from

**Step (3)**by 0.194 m/s

^{2}.

**(5) List some reasons why your values for the ball’s acceleration may be different from the accepted value for g.
**Amongst the reasons the ball’s acceleration might differ from standards are that the motion detector may not give 100% accurate data, and other factors exist such as air resistance.

Extension

**(1) Explain any differences between the upward motion and the downward motion.**

Analyzing the graphs of the volleyball, beach-ball, and rubber ball in separate halves revealed a distinct change in the magnitude of upward motion and downward motion. By writing out the Full Body Diagram for any given ball, the reason for these discrepancies is revealed: when any ball is traveling upward it has both gravity and fluid resistance pushing/pulling toward the earth, but on the ball’s return journey, the fluid resistance actually exerts a force upward. This is logical because fluid resistance is simply inertia of the air, which by opposing change will exert a force opposite the motion of the ball. Furthermore, fluid resistance at low speeds is equivalent to k multiplied by velocity, where k is a constant that is determined by factors such as size and shape, and can explain why the beach ball differs from the rubber ball, or the volleyball from the beach ball, as they all contain separate velocities and k values.

In conclusion, there exists definite and measurable mathematic patterns to a juggler’s toss of a ball.