AMERICAN PUBLIC UNIVERSITY | SCIN 233
AMU SCIN 233 (SCIN233) Physics I with Lab –
Labs 1–7 Complete Bundle | All-in-One PDF Study
SCIN 233 LAB 1 Guide | Updated 2026–2027
2-D Kinematics and
Projectile Motion
Institution American Public University
Course SCIN 233
Student ________________________________
Date September 4, 2026
DATA STATUS
The uploaded worksheet contained no recorded measurements. The numerical entries in this completed copy are a
model dataset chosen to be realistic and internally consistent with the worksheet equations. Replace them with
personally collected observations if the assignment requires original experimental data.
Assumptions used for the model calculations
Constant gravitational acceleration: g = 9.81 m/s2; ramp incline: 30.0 degrees; table height: 0.760 m; air
resistance neglected in theoretical predictions.
Completed answer key and calculation record
Lab 1 | Page 1
,AMERICAN PUBLIC UNIVERSITY | SCIN 233
Pre-Lab Questions
1. Predict the velocity of a marble at the bottom of a ramp after it starts from rest and travels
distance d.
Use vf2 = v02 + 2a d, with v0 = 0 and a = g sin(theta). Therefore:
vf = sqrt[2 g d sin(theta)].
2. Derive the time required for a ball dropped from rest at height h to reach the ground.
For vertical motion, h = v0yt + (1/2)gt2. Because v0y = 0, h = (1/2)gt2. Solving for the positive time gives:
t = sqrt(2h/g).
3. Write a general equation for the horizontal distance traveled from a table of height h at
horizontal speed v0x.
Horizontal acceleration is zero, so x = v0xt. Substituting the fall time from Question 2 gives:
x = v0x sqrt(2h/g).
Model calculation constants
Quantity Value How used
Ramp angle 30.0 degrees a = 9.81 sin(30 degrees) = 4.905 m/s^2
Table height 0.760 m t = sqrt[2(0.760)/9.81] = 0.3936 s
Lab 1 | Page 2
,AMERICAN PUBLIC UNIVERSITY | SCIN 233
Experiment 1: Distance Traveled by a Projectile
Table 1. Range at Ramp Distance 1
Ramp incline: 30.0 degrees Ramp distance: 0.200 m
Trial Measured horizontal distance (m)
1 0.533
2 0.527
3 0.538
4 0.531
Average 0.5323
Table 2. Range at Ramp Distance 2
Ramp incline: 30.0 degrees Ramp distance: 0.300 m
Trial Measured horizontal distance (m)
1 0.651
2 0.658
3 0.646
4 0.654
Average 0.6522
Table 3. Range at Ramp Distance 3
Ramp incline: 30.0 degrees Ramp distance: 0.400 m
Trial Measured horizontal distance (m)
1 0.748
2 0.756
3 0.751
4 0.745
Average 0.7500
Lab 1 | Page 3
, AMERICAN PUBLIC UNIVERSITY | SCIN 233
Experiment 1: Calculations and Analysis
Table 4. Velocity and Range Data for All Ramp Distances
Ramp distance Calculated velocity Predicted range Average actual
Percent error
(m) (m/s) (m) range (m)
0.200 1.401 0.551 0.5323 3.47%
0.300 1.716 0.675 0.6522 3.41%
0.400 1.981 0.780 0.7500 3.81%
Worked example for d = 0.200 m
v = sqrt[2(9.81)(0.200)sin(30 degrees)] = 1.401 m/s
Predicted range = vt = (1.401)(0.3936) = 0.551 m
Percent error = |0.5323 - 0.5514| / 0.5514 x 100 = 3.47%
2. How do the predictions compare with the observed data? Explain at least two reasons for the
differences.
The measured averages are slightly smaller than the predictions, differing by about 3.4% to 3.8%. First,
rolling friction and deformation remove mechanical energy, while the simplified velocity equation treats the
motion as lossless. Second, some energy becomes rotational kinetic energy, so the marble's translational
speed is lower than the point-particle prediction. Air resistance and uncertainty in the ramp angle, table
height, launch point, and landing mark also contribute.
3. Which hits the ground first: a horizontally fired pellet or an identical pellet dropped at the
same time?
Ignoring air resistance and assuming both begin at the same height, they hit the ground at the same time.
Their initial vertical velocities are both zero and each has the same vertical acceleration, -g. Horizontal
velocity does not change the fall time.
Lab 1 | Page 4
AMU SCIN 233 (SCIN233) Physics I with Lab –
Labs 1–7 Complete Bundle | All-in-One PDF Study
SCIN 233 LAB 1 Guide | Updated 2026–2027
2-D Kinematics and
Projectile Motion
Institution American Public University
Course SCIN 233
Student ________________________________
Date September 4, 2026
DATA STATUS
The uploaded worksheet contained no recorded measurements. The numerical entries in this completed copy are a
model dataset chosen to be realistic and internally consistent with the worksheet equations. Replace them with
personally collected observations if the assignment requires original experimental data.
Assumptions used for the model calculations
Constant gravitational acceleration: g = 9.81 m/s2; ramp incline: 30.0 degrees; table height: 0.760 m; air
resistance neglected in theoretical predictions.
Completed answer key and calculation record
Lab 1 | Page 1
,AMERICAN PUBLIC UNIVERSITY | SCIN 233
Pre-Lab Questions
1. Predict the velocity of a marble at the bottom of a ramp after it starts from rest and travels
distance d.
Use vf2 = v02 + 2a d, with v0 = 0 and a = g sin(theta). Therefore:
vf = sqrt[2 g d sin(theta)].
2. Derive the time required for a ball dropped from rest at height h to reach the ground.
For vertical motion, h = v0yt + (1/2)gt2. Because v0y = 0, h = (1/2)gt2. Solving for the positive time gives:
t = sqrt(2h/g).
3. Write a general equation for the horizontal distance traveled from a table of height h at
horizontal speed v0x.
Horizontal acceleration is zero, so x = v0xt. Substituting the fall time from Question 2 gives:
x = v0x sqrt(2h/g).
Model calculation constants
Quantity Value How used
Ramp angle 30.0 degrees a = 9.81 sin(30 degrees) = 4.905 m/s^2
Table height 0.760 m t = sqrt[2(0.760)/9.81] = 0.3936 s
Lab 1 | Page 2
,AMERICAN PUBLIC UNIVERSITY | SCIN 233
Experiment 1: Distance Traveled by a Projectile
Table 1. Range at Ramp Distance 1
Ramp incline: 30.0 degrees Ramp distance: 0.200 m
Trial Measured horizontal distance (m)
1 0.533
2 0.527
3 0.538
4 0.531
Average 0.5323
Table 2. Range at Ramp Distance 2
Ramp incline: 30.0 degrees Ramp distance: 0.300 m
Trial Measured horizontal distance (m)
1 0.651
2 0.658
3 0.646
4 0.654
Average 0.6522
Table 3. Range at Ramp Distance 3
Ramp incline: 30.0 degrees Ramp distance: 0.400 m
Trial Measured horizontal distance (m)
1 0.748
2 0.756
3 0.751
4 0.745
Average 0.7500
Lab 1 | Page 3
, AMERICAN PUBLIC UNIVERSITY | SCIN 233
Experiment 1: Calculations and Analysis
Table 4. Velocity and Range Data for All Ramp Distances
Ramp distance Calculated velocity Predicted range Average actual
Percent error
(m) (m/s) (m) range (m)
0.200 1.401 0.551 0.5323 3.47%
0.300 1.716 0.675 0.6522 3.41%
0.400 1.981 0.780 0.7500 3.81%
Worked example for d = 0.200 m
v = sqrt[2(9.81)(0.200)sin(30 degrees)] = 1.401 m/s
Predicted range = vt = (1.401)(0.3936) = 0.551 m
Percent error = |0.5323 - 0.5514| / 0.5514 x 100 = 3.47%
2. How do the predictions compare with the observed data? Explain at least two reasons for the
differences.
The measured averages are slightly smaller than the predictions, differing by about 3.4% to 3.8%. First,
rolling friction and deformation remove mechanical energy, while the simplified velocity equation treats the
motion as lossless. Second, some energy becomes rotational kinetic energy, so the marble's translational
speed is lower than the point-particle prediction. Air resistance and uncertainty in the ramp angle, table
height, launch point, and landing mark also contribute.
3. Which hits the ground first: a horizontally fired pellet or an identical pellet dropped at the
same time?
Ignoring air resistance and assuming both begin at the same height, they hit the ground at the same time.
Their initial vertical velocities are both zero and each has the same vertical acceleration, -g. Horizontal
velocity does not change the fall time.
Lab 1 | Page 4
