A. Height of a plane as it begins to
ascend
B. My experiment looks at the
trajectory of a flight as it takes off and accelerates until it eventually
reaches its flying altitude. What is the height of the plane at 5 seconds?
C.
Time in Seconds
|
Height in feet
|
0
|
0
|
1
|
60
|
3
|
200
|
5
|
595
|
7
|
1240
|
9
|
2500
|
D. Graph
E. Secant Lines from 1 second to 3,5 and 7 seconds
a.
(1,60)
and (3,200) = 70
b.
(1,60)
and (5,595) = 133.75
c.
(1,60)
and (7,1240) = 196.667
I noticed that the slope of the
lines continue to increase and it gets steeper as the plane continues its
upward trajectory.
F.
G. Point on the tangent line. Where time = 4
(3,200) to (5,595) = 197.5
(3,200) to (7,1240) = 310
(3,200) to (9,2500) =383.333
310+197.5/2= 253.75 height at
time=4
H. If I calculate the average rate of
change from 0 seconds to 9 seconds, I can realize that the rate of change is
277.778 feet per second. However, the plane didn’t travel at that exact rate at
every interval because in the first second, the plane only climbed 60 feet. I
know that by using the Instantaneous rate of change and by getting values closer
and closer to the tangent line, I can approximate the rate of change for that
specific time rather than getting the overall average rate of change. I know that the value from part G is the IRC
because I calculated the average rate of change from the two points and got it
to get closer and closer until it eventually approached the rate of change at
the tangent line. That point s the limit of the average rate of change and the
slope of that interval.
Very cool data to think about. I would assume that the initial rise reaches a plateau once the plane finds it's optimal altitude. I also wonder if the rate of change is the same at 9 seconds after take off and right before landing!
ReplyDeleteVery good job in the interpretation of your graphs and your data. It is a nice experiment to analyze and thing about. It is very clear and interesting!
ReplyDeleteGreat job projecting your thoughts and analysis on paper . It is clear to read and interesting to follow
ReplyDeletematthias,
ReplyDeletedefinitely a good topic, and a nice change to population growth. your graphs look good and your table is easy to interpret, but there were a few issues with some of your results.
i think your question should have been "what is the velocity at t = 5 seconds?", since you already know the height at t = 5 seconds. also, your question doesn't match the rest of your experiment, since you investigated what happens at t = 1 for your secant lines and you calculated a tangent line for the value t = 4 seconds. even though your actual calculations are correct, they don't match your question and you have essentially conducted two different experiments, since you looked at two different time values that aren't related to each other. also, remember to include the units for your secant and tangent calculations.
a little bit rocky on this one, but overall i can tell that you were getting to the right idea of the IRC. let me know if you have further questions.
professor little