Flying+Ball

=The Flying Ball Investigation= By: Alex Chun, Enoch Cheung, Jeremy Wong, Nathaniel Woo

Purpose
The goal of this task is to model the flight of a marble, from the end of the ramp until it hits the floor. To test the accuracy of your model the challenge will be to land your marble in a cup. Your instructor will place the stand with cup. By measuring the horizontal placement of the cup, you will determine the vertical placement from your model.

Equipment

 * TI-83 Calculator
 * Stopwatch
 * Measuring Tape
 * Standard Golf Ball
 * Arched Track (to release ball)
 * Ring Stand
 * Mug

Steps:

 * 1) Run several trials, always releasing the marble from the same spot.
 * 2) Make whatever measurements you deem appropriate.
 * 3) Create your model.
 * 4) Record the model.
 * 5) As an extension...consider the following: How does the position of release of the ball affect the ball's flight path? How does varying the weight or size of ball impact the ball's flight?

Data:

 * || Time (Seconds) || Horizontal Distance (Meters) ||
 * Trial 1 || 0.37 || 1.00 ||
 * Trial 2 || 0.39 || 1.02 ||
 * Trial 3 || 0.38 || 1.04 ||
 * Trial 4 || 0.37 || 1.01 ||
 * Trial 5 || 0.37 || 1.03 ||
 * Average || 0.376 || 1.02 ||

Finding the initial velocity:
x represents horizontal distance in centimeters y represents height in centimeters


 * Defining variables:**




 * Substituting these variables into the equations for horizontal distance and height:**




 * Combining these equations to find the initial velocity:**




 * From the Pythagorean Theorem,**




 * The initial velocity is 2.800 meters per second.**

Finding the initial angle:

 * Defining variables:

**

1. In terms of y (vertical position)

 * Defining Variables:



Substituting into equation:

**

2. In terms of x (horizontal position)

 * Defining Variables:



Substituting into equation:

**

The Mug Challenge

 * Assuming the horizontal position of the cup is 0.8m away from the point of release, we have to determine the vertical placement from our model.**

Determining the point in time in which the ball is 0.8m from the point of release:

 * Defining Variables:**




 * Substituting into equation and solving for x:

At 0.295 seconds, the ball is 0.8 meters from the point of release.**

Determining the vertical position of the ball at 0.295 seconds:

 * Defining Variables:



Substituting into equation and solving for y: Conclusion: For the ball to land in the cup, the mouth of the cup would have to be 0.732m above the ground**.