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Intro:
This experiment was performed to see the relationship between horizontal velocity and vertical velocity on an object when it is launched off a table with only a horizontal speed and another time when it is launched at an angle. Also to see how both the vertical and horizontal positions are related to each other. Just a two pictures on a computer was used to conduct this experiment, along with excel to record the data gathered from those pictures. The key concepts of this experiment were to show how horizontal velocities remain constant when a ball is launched with or without an angle and how gravity affects the vertical velocity. This experiment was performed through gathering and graphing data from a picture that showed a balls location every 1/24 of a second
Intro
This experiment was performed to see the relationship between horizontal velocity and vertical velocity on an object when it is launched off a table with only a horizontal speed and another time when it is launched at an angle. Also to see how both the vertical and horizontal positions are related to each other. Just a two pictures on a computer was used to conduct this experiment, along with excel to record the data gathered from those pictures. The key concepts of this experiment were to show how horizontal velocities remain constant when a ball is launched with or without an angle and how gravity affects the vertical velocity. This experiment was performed through gathering and graphing data from a picture that showed a balls location every
1/24
of a second.
Materials
The materials used for this experiment was just two pictures to gather data from.
Results
Part 1 Horizontal Launch
Part 1-1
Method
The method used for the first part of part one, was just to record the x-axis position for each time frame there was. Then make a position vs time graph with the data gathered.
Time
(seconds)
X-Position(meters)
0
0
0.
1025
2/24
0.205
3/24
0.3075
4/24
0.41
5/24
0.5125
6/24
0.615
7/24
0.7175
8/24
0.8175
9/24
0.92
10/24
1.02
11/24
1.12
Part 1-2
Method
The method used for the second part of part one, was to record the y-axis position at each time frame and then use the data gathered to complete a table to find its displacement , the delta t, and the velocity at each 1/24th of a second.
Time(seconds)
Y-Position
Vy
0
1.09
1/24
2/24
1.08
-0.035
-0.42
2/24
2/24
1.055
-0.0625
-0.75
3/24
2/24
1.0175
-0.1
-1.2
4/24
2/24
0.955
-0.145
-1.74
5/24
2/24
0.8725
-0.175
-2.1
6/24
2/24
0.78
-0.2025
-2.43
7/24
2/24
0.67
-0.24
-2.88
8/24
2/24
0.54
-0.28
-3.36
9/24
2/24
0.39
-0.3375
-4.05
10/24
2/24
0.2025
-0.35
-4.2
11/24
0.04
Type of Launch
X-Axis
Y-Axis
Xo
Vox
a
Yo
Voy
a
Horizontal Launch
0
2.4468m/s
0
1.09m
0
-10.42m/s2
Part 1-3
Method
The method was to make a velocity of y vs time graph with the data from the chart.
Part 1-4
Methods
The method used for this part of part one was to use the data collected to find the distance the ball lands at x and y and then to compare it to what the picture says.
A) x = 11/24 * 2.4468
x = 1.12145m
B) Yes the calculated value is close to the value on the picture. The calculated value is off by about .00145 meters. Which is above the measured value.
C) x = 0 + (1/2)(-10.425)(11/24)2
x = 0.0456m
D) Yes the calculated value is close to the value on the picture. The calculated value is off by about .005 meters from the picture
Part 2
Part 2-1
0
.02
1/24
.09
2/24
.16
3/24
.23
4/24
.3025
5/24
.375
6/24
.4675
7/24
.5175
8/24
.58
9/24
.66
10/24
.73
11/24
.80
12/24
.87
13/24
.95
14/24
1.0025
15/24
1.08
16/24
1.1525
Part 2-2
Time(seconds)
Y
Vy
0
0.785
1/24
2/24
0.8725
0.16
1.92
2/24
2/24
0.945
0.055
0.66
3/24
2/24
1
0.085
1.02
4/24
2/24
1.03
0.05
0.6
5/24
2/24
1.05
0.02
0.24
6/24
2/24
1.05
-0.0175
-0.21
7/24
2/24
1.0325
-0.05
-0.6
8/24
2/24
1
-0.0785
-0.942
9/24
2/24
0.954
-0.1575
-1.89
10/24
2/24
0.8425
-0.164
-1.968
11/24
2/24
0.79
-0.16
-1.92
12/24
2/24
0.6825
-0.2275
-2.73
13/24
2/24
0.5625
-0.26
-3.12
14/24
2/24
0.4225
-0.2925
-3.51
15/24
2/24
0.27
-0.3225
-3.87
16/24
0.1
0.
Type of Launch
X-Axis
Y-Axis
Xo
Vox
a
Yo
Voy
a
Angled Launch
.02m
1.6948m/s
0
.775m
2.0793m/s
-9.4834 m/s2
Part 2-3
Methods
The methods used for this part is to use the data from the graphs to find when the ball reaches is peak, compare the height the ball reaches from the picture and our math, and to find the angle the ball was thrown at.
A) 0 = -9.5019x + 2.0793
-2.0793 = -9.5019x
0.2188s = x
The ball will reach its peak around 0.2188 seconds.
B) x = .785 + 2.0793* 0.2188 + (1/2)* -9.5019 * 0.21882
x = .785 + 0.227552
x = 1.012552m
= ((1.055-1.012552)/1.055)*100
= ((0.042448)/1.055)*100
= 0.04023 * 100
= 4.02%
Questions
Horizontal Launch
1. The initial position along the x-axis is at 0 meters.
2. The initial Vx is 2.446 m/s.
3. There is no acceleration along the x-axis, so the velocity will remain constant.
4. The initial position along the y-axis is at 1.09 meters.
5. The initial Vy is 0 m/s. This happened because the ball was released with only a horizontal speed.
6. The acceleration due to gravity, gotten from the graphs was -10.425 m/s2 . The percentage error is 6.37%.
= ((g-|-10.425|) / g) * 100
= ((9.8-|-10.425|) / 9.8) * 100
= (.625/9.8) * 100
= 0.0637 * 100
= 6.37%
7. y = -2.3024x + 1.252
0 = -2.3024x + 1.252
-1.252 = -2.3024x
x = .5438s
The ball reaches the ground near .5438 seconds
8. Vfinal = Vinitial + a*t
Vfinal = 0 + -10.425 * .5438
Vfinal = -5.669 m/s
The vertical velocity the ball hits the ground with would be -5.669 m/s, using the gravity that was found and the amount of time it takes to reach the ground.
Angled Launch
1. The initial position along the x-axis is at .02 meters.
2. The initial Vx is 1.6948 m/s.
3. The acceleration is 0 m/s2, because there is no other acceleration acting on the horizontal velocity, which makes it remain constant.
4. The starting position for the y-axis is .775 meters.
5. The starting velocity for y is 2.24583m/s.
6. The acceleration acting on the ball is -9.4834 m/s2. The percentage of error from gravity we got and the actual constant is 3.23%
= ((g-|-9.4834||) / g)*100
= ((9.8-|-9.4834||) / 9.8)*100
= (.3166/9.8)*100
= 0.0323 * 100
= 3.23%
7. Using y = -4.9712×2 + 2.2739x + 0.7891 and the quadratic equation to find what time y would be equal to 0. Which results in about .687 seconds. The ball will reach the ground around .687 seconds.
8. 0 = 2.07 -9.5*t
t = 0.2178s
Vfinal = Vinitial + a*(.687-2t)
Vfinal = 2.07 + -9.5*0.1434
Vfinal = -0.7077 m/s
The speed the ball hits the ground with is about -0.7077 m/s
9. tan-1(2.07/1.69) = 50.77
The angle the ball was thrown at was 50.77 degrees. The percentage error is 7.69%
= ((55-|50.77|)/55)*100
= (4.23|)/55)*100
= .0769*100
= 7.69%
Conclusion
Y-Velocity
vs Time (m/s)
0.0 0.0416666666666667 0.0833333333333333 0.125 0.166666666666667 0.208333333333333 0.25 0.291666666666667 0.333333333333333 0.375 0.416666666666667 0.458333333333333 0.5 0.541666666666 667 0.583333333333333 0.625 0.666666666666667 1.919999999999999 0.660000000000001 1.020000000000001 0.600000000000001 0.24 -0.210000000000001 -0.600000000000001 -0.942 -1.889999999999999 -1.967999999999999 -1.92 -2.73 -3.12 -3.51 -3.87 Time
Y-Velocity
Position-X vs Time
0.0 0.0416666666666667 0.0833333333333333 0.125 0.166666666666667 0.208333333333333 0.25 0.291666666666667 0.333333333333333 0.375 0.416666666666667 0.458333333333333 0.0
0.1025
0.205 0.3075 0.41 0.5125 0.615 0.7175 0.8175 0.92 1.02 1.12 Time
X-Position(meters)
Position-Y vs Time
0.0 0.0416666666666667 0.0833333333333333 0.125 0.166666666666667 0.208333333333333 0.25 0.291666666666667 0.333333333333333 0.375 0.416666666666667 0.458333333333333 1.09 1.08 1.055 1.0175 0.955 0.8725 0.78 0.67 0.54 0.39 0.2025 0.04 Time
Y-Position(meters)
Velocity(Y) vs Time (m/s)
0.0 0.0416666666666667 0.0833333333333333 0.125 0.166666666666667 0.208333333333333 0.25 0.291666666666667 0.333333333333333 0.375 0.416666666666667 0.458333333333333 -0.420000000000002 -0.75 -1.199999999999999 -1.74 -2.099999999999999 -2.43 -2.88 -3.36 -4.050000000000001 -4.200000000000001 Time
Y Velocy
X-Position vs Time
X-Position 0.0 0.0416666666666667 0.0833333333333333 0.125 0.1666666 66666667 0.208333333333333 0.25 0.291666666666667 0.333333333333333 0.375 0.416666666666667 0.458333333333333 0.5 0.541666666666667 0.583333333333333 0.625 0.666666666666667 0.02 0.09 0.16 0.23 0.3025 0.375 0.4675 0.5175 0.58 0.66 0.73 0.8 0.87 0.95 1.0025 1.08 1.1525 Time
X-Position(meters)
Y-Position vs Time
0.0 0.0416666666666667 0.0833333333333333 0.125 0.166666666666667 0.208333333333333 0.25 0.291666666666667 0.333333333333333 0.375 0.416666666666667 0.458333333333333 0.5 0.541666666666667 0.583333333333333 0.625 0.666666666666667 0.785 0.8725 0.945 1.0 1.03 1.05 1.05 1.0325 1.0 0.954 0.8425 0.79 0.6825 0.5625 0.4225 0.27 0.1 Time
Y-Position(meters)
