M3.1 Laboratory Report 3- Zhiyuan Wu
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Aerospace Engineering
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Apr 3, 2024
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M3.1 Laboratory Report 3
Name: Zhiyuan Wu
Date: 1/29/2024
Propose: Use a computer simulation to investigate what projectile
motion is.
Introduction: Kinematics equations
，
gravitational acceleration
Procedure: Use a computer simulation, input angle, initial speed and
so on. Then see the vectors of acceleration.
Data and Data Evaluation:
Part 1
Pumpkin:
Initial Speed
Time
Range Height
2 m/s
1.28 s
2.55 m
0 m
4 m/s
1.28 s
5.11 m
0 m
6 m/s
1.28 s
7.66 m
0 m
8 m/s
1.28 s
10.22 m
0 m
10 m/s
1.28 s
12.77 m
0 m
12 m/s
1.28 s
15.33 m
0 m
14 m/s
1.28 s
17.88 m
0 m
16 m/s
1.28 s
20.43 m
0 m
18 m/s
1.28 s
22.99 m
0 m
20 m/s
1.28 s
25.54 m
0 m
These values show with the increase of initial speed, the range is
increasing, but the time of landing is not change.
Car:
Initial Speed
Time
Range Height
2 m/s
1.28 s
2.55 m
0 m
4 m/s
1.28 s
5.11 m
0 m
6 m/s
1.28 s
7.66 m
0 m
8 m/s
1.28 s
10.22 m
0 m
10 m/s
1.28 s
12.77 m
0 m
12 m/s
1.28 s
15.33 m
0 m
14 m/s
1.28 s
17.88 m
0 m
16 m/s
1.28 s
20.43 m
0 m
18 m/s
1.28 s
22.99 m
0 m
20 m/s
1.28 s
25.54 m
0 m
Comparing the two results, I find with the same initial speed,
whatever the object is, the time to landing and range will not
change.
Part 2
investigating gravitational acceleration
The direction of the vector is down, and it represents gravitational
acceleration.
The length of the vector doesn’t change throughout its flight.
It can tell me the direction and magnitude of the acceleration acting
on the cannonball throughout its duration of flight.
If we change the angle of the cannon, I think the acceleration vector
will not change, because the gravitational acceleration is constant.
The acceleration vector does not change its length and direction at
new angle, my prediction is right.
Discovery: The launch angle affects the trajectory and range of the
projectile but does not affect the gravitational acceleration acting on
it.
investigating velocity
Angle 45 degree:
The length of the velocity vector in the y-direction decreases as the
cannonball rises, becomes zero at the peak of its trajectory, and
then increases as the cannonball falls back down.
Initially upward, it becomes zero at the peak, and then downwards
as the cannonball descends.
The velocity vector in the y-direction becomes zero at the peak of
the trajectory. This is the highest point of the flight, where the
cannonball momentarily has no vertical motion.
Ascent: On leaving the cannon, the vertical component of velocity is
maximum and positive. It decreases due to gravity.
Peak: At the peak, all the upward velocity is counteracted by
gravity, making the vertical velocity zero.
Descent: After the peak, the cannonball gains downward velocity,
increasing in magnitude until it hits the ground.
The velocity in the x-direction remains constant throughout the
flight.
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Angle 65 degree:
When the angle is changed to 65 degrees and the experiment is
repeated, the general observations regarding the y and x-direction
velocities remain the same.
However, the specifics change:
The
initial vertical component of the velocity is higher, and the time to
reach the peak is longer due to the steeper angle. The cannonball
reaches a higher altitude.
The horizontal component of velocity is
lower compared to the 45-degree launch, resulting in a shorter
range despite the higher altitude.
Part 3
Result and conclusion: Mass of the Projectile: Contrary to intuition,
the mass of the projectile did not significantly affect its trajectory in
a vacuum. All objects accelerate at the same rate, regardless of
mass, as long as external forces like air resistance are negligible.
Type of Object Shot: The shape and size of the projectile had no
impact on the trajectory under ideal conditions (no air resistance).
However, when air resistance was factored in, these attributes
became crucial, influencing the range and stability of the projectile's
flight.
Gravity: Stronger gravity resulted in a shorter range and a more
pronounced parabolic trajectory, whereas weaker gravity extended
the range and flattened the trajectory.
Diameter of the Projectile: Under vacuum conditions, the diameter
did not affect the projectile’s motion. However, with air resistance, a
larger diameter increased the air resistance, affecting both the
range and the flight path.
Altitude of Launch: Higher altitudes, where air density is lower,
demonstrated slightly increased ranges due to reduced air
resistance, emphasizing the role of atmospheric conditions in
projectile motion.
Air Resistance: The inclusion of air resistance in my simulations
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significantly altered projectile trajectories, reducing range and
modifying the path, especially during the descent phase.
Drag Coefficient: Adjusting the drag coefficient underscored the
impact of aerodynamic properties on projectile motion. A higher
drag coefficient increased the effects of air resistance, reducing the
range and speed, and vice versa.