Blog Post 2

1.     Recorded data from a ball being thrown from one person and being caught by another person (time vs. height).

2.     My brother and I were watching the Patriots versus Seawhawks Super Bowl Game a few weeks ago. My brother is very familiar with different NFL players’ career statistics (ex. Passing, rushing, receiving, etc.) as he is a huge fan of the Patriot’s quarterback Tom Brady. He wanted to find the instantaneous rate of change of one of his passes during the game at T=5 seconds when one of receivers, Rob Gronkowski, catches it near the end zone.

3.      

Time (t in seconds)	H (in feet)
0	5
1	22
2	36
3	48
4	55
5	70
6	62
7	54
8	49
9	32
10	26
11	14
12	6

4.     Average Rate of Change: (Y2-Y1)/(X2-X1)

5.     (5,70) and (3,48): (70-48)/(5-3)= 22/2= 11 ft/s.

6.     (5,70) and (7, 54): (70-54)/(5-7)=16/-2= -8 ft/s.

7.     (5,70) and (12,6): (70-6)/(5-12)= 64/ -7= -9.14 ft/s.

8.     To find the rate of change I needed to use slope formula. My brother wanted to see what the instantenous rate of change was at 5 seconds for Brady’s pass (5, 70). I took various points from the chart from when he threw it to when it was falling into the receiver’s hands. Before the 5 seconds, on the left side, the slope values are all positive and get larger per value input closest to 5 seconds.  And after the 5 seconds, on the right side of the graph, the slove is all negative with the values getting smaller as the time increases.

9.     See above graph for tangent line drawn.

10.  In order to find the instantenous rate of change, it is necessary to make a tangent line at t=5. Now, we need to find a point close to the points at (5,70). We can use the points (5.4,66). So now we have the points (5,70) and (5.4, 66). We calculate slop again (70-66)/(5-5.4)= 4/-.4= -10 ft/s.

11.  My brother can conclude from this that at t=5, the instaneous rate of change (IRC) is 10 ft/s. The negative just means that the ball is falling downwards at this point. The IRC is the same thing as the derivative of the slope or giving us the exact speed of how fast the ball was going at 5 seconds. ARC was becoming larger from the left side and positive as the ball was going up in the air and from the point 5 seconds the ARC became negative and smaller and smaller because the ball was coming back down.