Blog #2
Ricardo Zapata
I chose the experiment of the ball bounce.
b.Write a narrative or synopsis explaining your application/experiment and include a question. (for example, what is the velocity of the snowball at exactly 2 seconds? Or how can I find the velocity of the baseball at exactly 3 seconds?)
This is an experiment in which the ball for time(s) goes up to some height(cm). The results
of this experiment can be seen in the table below.
What is the velocity of the ball at 0.53 seconds?
This means that at points like (0.23,40) and (0.30,141) the ball is in a lower height and is in process to get to the height of the point (0.53,146), this is the reason why the slope is positive, because the point has to increase. And in point (0.46,178) the ball has a higher height, and this is why the slope is negative, because it has to get to an inferior height to get to the point (0.53,146).
This calculation means that the ball is going to decrease 800 centimeters for every second that passes.
h.Explain in detail how you know that the value from part g is the IRC. (i.e. since the values of calculations from part d are getting smaller and smaller, this shows that the slope of the secant is getting closer and closer to the tangent line … or some explanation similar to this). BE DETAILED!!!
The values of the maximum height keeps getting smaller and smaller, as time increases, so the speed will decrease. This is why the slope of the point in the tangent is negative. So the ball will decrease 800cm/sec until it comes to a complete stop.
b.Write a narrative or synopsis explaining your application/experiment and include a question. (for example, what is the velocity of the snowball at exactly 2 seconds? Or how can I find the velocity of the baseball at exactly 3 seconds?)
This is an experiment in which the ball for time(s) goes up to some height(cm). The results
of this experiment can be seen in the table below.
What is the velocity of the ball at 0.53 seconds?
c.Create a table of values for the data that you have recorded from your application/experiment.
d.Graph the points using the data from your table of values (connect the dots).
e.Calculate the slope (ARC) of at least three secant lines originating from the same point on your graph to three different points on your graph (i.e. maybe you want to know what happens exactly at x = 20, so your points might be (20, 62), (20, 56), (20, 50)). Explain what you notice about the ARC of these secant lines and what the calculations mean/represent in terms of your experiment/application.
f.Sketch an approximation of a tangent line that passes though the same point (P) from part e to which you connected your secant lines (i.e. you would draw a tangent line through the point 20, since that is the same point that you used to calculate your three different secant lines)
g.Choose a second point (Q) on the tangent line, and calculate the slope of the line (PQ). This calculation will be the instantaneous rate of change ((IRC or derivative at a point)…be sure to identify the units correctly). Explain what this calculation means mathematically and in terms of your experiment/application.
This calculation means that the ball is going to decrease 800 centimeters for every second that passes.
h.Explain in detail how you know that the value from part g is the IRC. (i.e. since the values of calculations from part d are getting smaller and smaller, this shows that the slope of the secant is getting closer and closer to the tangent line … or some explanation similar to this). BE DETAILED!!!
The values of the maximum height keeps getting smaller and smaller, as time increases, so the speed will decrease. This is why the slope of the point in the tangent is negative. So the ball will decrease 800cm/sec until it comes to a complete stop.
How come your graph only shows the ball hitting the ground once? I did the same experiment and there were three intervals of the ball bouncing within the 1.6 seconds.
ReplyDeleterachel,
Deletegood job of noticing that data was truncated.
professor little
I agree with what Rachel said. You could flesh out your part H by using the terms IRC and how that is shown in your example problem.
ReplyDeleterhea,
Deletei like that you gave ricardo pointers on how he could add more spice to his post by using appropriate math language! constructive, yet encouraging. =]
professor little
ricardo,
ReplyDeletenice choice from the example folder! your table looks good and your graphs. i like how you explained in detail the meaning of each secant calculation. remember to include the units after each calculation, though, you forgot that part. :/ you could have added a little more detail to your IRC explanation, but other than those couple of things, good job. =]
professor little