Experiment two_ Projectile motion
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University of Illinois, Urbana Champaign *
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Course
102
Subject
Physics
Date
Apr 3, 2024
Type
Pages
5
Uploaded by DrBookPony31
Alexis Ortiz
A20532815
Experiment two: Projectile motion
Part 1:
(a) What are the two initial velocities for the first two firing settings (the first two “clicks”)?
Make a table consisting of the initial velocities, its components vx and vy, the launch angles,
the time of flight, and the horizontal range.
(Setting 1)
Trials
Launch
angle ( º)
Time of flight
(m/s)
Range
(m)
Initial Velocity
(m/s)
V
ix
(m/s)
V
iy
(m/s)
Trial 1
20
0.400
1.027
3.957
3.718
1.353
Trial 2
20
0.600
1.018
3.940
3.702
1.348
Trial 3
20
0.550
1.019
3.942
3.704
1.348
Average
20
0.517
1.021
3.946
3.708
1.350
The average initial velocity of the ball on setting one is 3.946 meters per second.
(Setting 2)
Trials
Launch
angle ( º)
Time of flight
(m/s)
Range
(m)
Initial Velocity
(m/s)
V
ix
(m/s)
V
iy
(m/s)
Trial 1
20
0.3
1.186
4.252
3.996
1.454
Trial 2
20
0.3
1.174
4.231
3.976
1.447
Trial 3
20
0.32
1.179
4.240
3.984
1.450
Average
20
0.31
1.180
4.241
3.985
1.450
The average initial velocity of the ball on setting two is 4.241 meters per second.
(b) Consider the angle that gave you the longest range. Using the angle and initial velocity
calculate the maximum height (ymax) reached at this angle? What is the overall maximum
height reached in your experimental data? Which angle gave you the maximum height?
(*These results came from Part 2 of the lab due to time constraints resulting in a lack of full data in part 1)
(c) Make a graph of launch angle vs. horizontal range for the second experiment. Label the
axes appropriately with correct units.
(on Setting 1)
Alexis Ortiz
A20532815
The overall maximum height reached from this data was 0.201 meters high. An angle of
65
gave the maximum height. An angle of 55
∘
gave the maximum range.
° (d) For the third experiment, how do your measured values of the gravitational
acceleration compare to the accepted value of g = 9.8 m/s2 ? What are possible sources of
error for this experiment?
(* Due to equipment malfunction, Part 3 of this experiment had no data taken.)
To find the experimental value of gravitational acceleration, a free fall experiment would
be conducted. Acceleration would be calculated using equation 1, with the initial height being
the height of the table (
, the time measurement being the time to hit the ground (t), and the
𝑦
𝑖
) final height being 0 meters (
). Had the experiment been conducted, the ball would be released
𝑦
? from rest over a photogate, which will start the measurement of total time. Then, the ball would
pass the time of flight sensor on the ground. This time would be used in equation 2 to determine
gravity. Possible sources of error that could arise from this experiment include air resistance
dragging on the ball, resulting in a higher acceleration than is accurate, or the ball falling at an
angle due to it being let go improperly.
Alexis Ortiz
A20532815
(e) If the steel ball is shot vertically upward, how long would it take for it to hit the floor
below? Calculate for both initial velocities.
Assuming the ball starts at 0 meters and ends its trajectory at 0 meters, the time it would
take for the ball to hit the floor would be 0.272 seconds for setting one and 0.296 seconds for
setting two, based on the equation
(equation 1)
𝑦
?
= 𝑦
𝑖
+ 𝑣
0
𝑡 +
1
2
𝑎𝑡
2
2. Ideally, what kind of mathematical curve is the projectile motion trajectory? Describe
two examples of projectile motion which you have observed or experienced outside of this
physics lab that follow this mathematical curve.
The mathematical curve of projectile motion trajectory is a parabolic curve. Two
examples of parabolic curves are the path of fireworks and the path of a punted football. They
both reach a maximum height, then fall to their original position height.
3. Are there two different launch angles that would give you the same range? Are there two
different launch angles that would give you the same height? Explain.
Yes, two different launch angles can result in the same range if they add up to 90 °
(complementary angles), as range is calculated with two times the sine of
∅
. This is due to the
smaller angle going faster, thus having less time in the air, and the larger angle going higher, thus
having less distance covered. Also, two different launch angles result in the maximum height if
they add up to 180°(supplementary angles), as height is calculated with the sine of
∅
. This can be
shown with their hypotenuses being the same.
4. If the steel ball is shot horizontally off the table, how much time would it take the ball to
hit the ground for each of the velocity settings of the launcher? Explain your answer using
the equations of motion and your experimental data. How does this relate to the ball being
dropped vertically from the table top to the floor below?
(equation 2)
𝑡 =
2𝑦
𝑖
?
The time to reach the ground could be calculated by taking the square root of two times
the initial height divided by the gravitational acceleration. The time to reach the ground cannot
be calculated with the partia data from this experiment, due to a missing measurement of the
height of the table.
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Projectile motion
Answer these two questions :
David has done the projectile experiment and he made the following table
Q1 : Connection between David's results and the projectile
what is the connection between David's results and abou
Lunching
angle 0
(*)
Range
Sin(20) Trial 1 sx Trial 2 sx
(m)
5.03
Range
Average
20
Range
projectile in general (what did you find ).
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30
0.8660
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5.69
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* Launch angles and ranges for an 85 kg human cannonball,
* For the first trial :
Second trial
10
40
20
Sin20
Stn20
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o 02 04 06 0.8 10 12 14 16 L8 20
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Express your answer using two significant figures.
m
Submit
Request Answer
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Express your answer using two significant figures.
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Submit
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If the experimental package comes to rest over a distance of 0.74 m upon hitting the air bags, what is the average stopping acceleration?
Express your answer using two significant figures.
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