Falling Objects I.

Note: you pay work on this homework assignment jointly with one other person in class. This will be true for all assignments.

In class on Tuesday, Oct 6 we made several measurements of the time of flight of tennis balls that were dropped from the fourth floor of Willamette Hall. Using that data do the following procedure.

1. Calculate the differences in height between the various floors where the timing measurements were made.

   The measured data are as follows:

   Floor	Meters
   4	0
   3	4.0
   2	7.95
   1	13.85

2. Determine by averaging the data any way you want, the time of flight the ball takes from one floor to the next. Explain how you averaged the data.

   The measured data are as follows:

   Floor-Floor	Seconds
   4 - 3	0.83,0.94,0.78,0.63,0.57,0.60,0.78,0.69, 0.72,0.68,0.72,0.97,0.82,0.59,0.72
   4 - 2	1.03,1.03,0.97,1.03,0.97,0.94,0.87,0.93,1.00 1.00,0.91,1.41,0.97,1.28,1.12,1.19
   4 - 1	1.50,1.47,1.25,1.81,1.44,1.56,1.50,1.57,1.69 1.50,1.56,1.60,1.60,1.53,1.50,1.49

3. Determine the average velocity of the ball between the floors 4-3, 3-2, 2-1, and 4-1. The average velocity is found by taking the total distance travelled and dividing that by the time it took to go from Point A to Point B.

4. Now take a critical look at the data to see if you can spot if there are any systematic errors in it.

5. Make a plot of average velocity of the ball vs. height above the atrium floor. For your height, pick the midpoint between the 2 floors you have used to determine the average velocity. Describe this plot (that is, is the average velocity the same as a function of height above the floor, increasing, decreasing).

   Determine the height above the atrium floor in which the instantaneous velocity of the ball will be the same as the average velocity of the ball between Floors 4 and 1. The instantaneous velocity of the ball is the velocity at a specific instant in time. You could not measure this from your experimental data. However, if you make a graphical representation of the data you can estimate instantaneous velocity by interpolating through the data. This is one of the reasons that graphs are so powerful but be warned, your ability to interpolate is only as good as the quality of your data.

6. Make another plot that involves time versus distance. That is, plot the total distance a ball has travelled versus the time it gets there. On the basis of that graph, try and estimate how long it would have taken the ball to fall a total distance of 50 meters.

7. Using intervals of approximately 1 second, determine the change in the velocity of the ball from your data. That is, how much faster will the ball be moving at 1 second compared to at 2 seconds from the time it is initially released from the top floor>

   Now let's use the JAVA applet and do something similar.