Project 2 (Parabolic motion) Start Example (1)
.docx
keyboard_arrow_up
School
University of Toledo *
*We aren’t endorsed by this school
Course
1240
Subject
Mathematics
Date
Apr 3, 2024
Type
docx
Pages
5
Uploaded by ColonelTarsierPerson391 on coursehero.com
Project 2: Parabolic motion
SHOW ALL WORK!!!
1.) Choose any object that you can safely throw that is heavy enough to not be influenced by wind and without wings, fins, or parachutes etc. Have someone record you tossing the object from left to right
in the air at any rate and at any trajectory you wish (Just not straight up). Be sure you record the throw alongside a wall suitable for identifying three specific locations that the object traveled through before and as it hits the ground (Horizontal distance from thrower’s hand, Vertical distance from the ground.) You could use a brick wall, chalkboard with a grid, or blank wall with painter’s tape for example. Post a link to your video. (10 pts) https://youtu.be/b6MOZM-WoCk
Notice that I used a background with a lot of detail, so I can easily pinpoint and measure three locations that the ball travels pass.
2.) You are going to measure three locations the object traveled through. You may use any unit of measurement you wish but be sure to measure it carefully
a.) By looking at your video, then physically measuring the spot on the background the object covers, how high was the object the moment you released it from your hand? This will be your first point (
0
, y
1
)
.
(5 pts) Pausing the video at the release point, and measuring the spot on the window that the ball is covering, I get the first point to be (0, 3.6’) since the ball is 3.6 feet high the moment I throw it.
b.) Next, carefully pinpoint and measure where the object reaches its maximum height. How far out from your hand was it when it reached its maximum height? How high did your object travel? This will be your second point ¿
(5 pts) Pausing at what I think is the highest point of the throw, I measure the spot on the window that the ball is covering. How far to the right did the ball travel from point 1? How high from the floor is the object? I got the point (2, 4.5)
c.) Lastly, measure how far horizontally from the thrower’s initial release point did the object travel when it landed. This will be your third point (
x
3
,
0
)
. (5 pts)
Lastly, I stop the video at the moment that ball hits the ground, and I measure horizontally over from the first point to that landing point and got the point (6,0).
3.) Using the three points from problem 2, create a parabolic model H(x) in the standard form
H
(
x
)=
a x
2
+
bx
+
c
for the path of your object where H(x) is the height when the object is x units from the thrower. (15 points)
a. List the three equations that your three measured points produced. (5 pts)
3.6
=
a
(
0
)
2
+
b
(
0
)
+
c
4.5
=
a
(
2.5
)
2
+
b
(
2.5
)
+
c
0
=
a
(
6
)
2
+
b
(
6
)
+
c
b. Solve these three equations for a, b, and c and write your parabolic model. (10 pts)
a
=−
.27
,b
=
1.05
,c
=
3.6
y
=−
.27
x
2
+
1.05
x
+
3.6
4.) Set your model from problem 3 to zero and solve by using the quadratic formula. You will have 2 solutions. (10 pts)
a. One of these solutions should be very close to your measurement in problem 2c. How accurate was your model? (If your model’s solution estimate and your actual measurement from problem 2 are not close, you made a mistake somewhere and must correct it before proceeding). (5 pts)
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help