Catapult Project
“Fling Queens”
Jenna Bohr, Meredith Hopkins, Kirsten Krause, & Julia Rutkowski
November 6, 2017
G/H Block
Marshmallow Catapult
Introduction:
A catapult is a “device in which accumulated tension is suddenly released to hurl an
object some distance” that uses potential (stored) energy as its power to launch projectiles. The
only force acting upon the projectile fired from the catapult is gravity, which has a known value
of -9.8 m/s². This means that when a projectile is fired, it will have both horizontal and vertical
velocity, resulting in a shape that generally looks like an arch. The horizontal velocity of a
projectile fired from a catapult remains constant throughout its flight time, assuming negligence
of air resistance. When a catapult is fired, the projectile will also have vertical and horizontal
components of its motion that can be determined by the initial velocity and angle (direction) of
the projectile.
The purpose of this investigation is to adjust the initial velocity and/or angle (direction)
from which a projectile (in this case, a marshmallow) is fired from a catapult in order to
accurately hit a target at a given distance. In order to do this, our group will use collected data
that compares the distance the arm of the catapult was from the ground (when pulled back) to the
distance the marshmallow was launched, to determine approximately how far the arm of the
catapult should be from the ground to fire the marshmallow the desired distance. The goal is to
hit the target in any area within two shots, and to hit the bullseye of the target within four shots.
Methodology:
First, two different types of wood were acquired. A sample catapult was printed from the
internet. The dimensions on the image were multiplied by four to reach the full size dimensions.
The base was cut to the proper length and assembled together without being drilled yet. On the
longer sides of the base towards one end, holes were drilled in the wood to place the bar in which
the arm pivots on. The arm was cut with a drilled hole and slipped onto the bar. Then the upright
fixtures were cut and assembled. Once each piece was in the desired spot, it was all drilled
together. Three rubber bands in each direction were assembled to the front base of the catapult. A
tennis ball was cut in half and drilled to the arm to be used as the holder for the projectile. After
testing the catapult a few times, two rubber bands were taken off to create a stronger tension with
the arm. In addition, a stiff foam bar was added to the front of the arm to allow the projectile to
be released at approximately 45°.
Results:
Firing distance of approx. 3 meters:
Trial # ΔX (meters) t (seconds)
1 3.0m .56s
2 3.3m .60s
3 3.4m .58s
4 3.5m .61s
Average Time: .59 seconds
Firing distance of approx. 5 meters:
Trial # ΔX (meters) t (seconds)
1 5.1m .73s
2 5.4m .88s
3 5.0m .78s
4 5.3m .83s
Average Time: .81 seconds
Firing distance of approx. 7 meters:
Trial # ΔX (meters) t (seconds)
1 6.8m 1.32s
2 7.3m 1.03s
3 6.8m 1.20s
4 7.2m 1.29s
Average Time: 1.21 seconds
Discussion and Analysis:
Line of best fit: y = -2.91286x + 27.9074
Variables:
X = height of the arm in centimeters from the ground
Y = horizontal distance projectile travels
Calculations:
Velocity and Angle at 3 meters:
Vxo = 5.01 m/s
Vyo = 2.9 m/s
ΔX = 3 meters
t = .59 seconds (.295 s at max height)
Vy = 0 m/s (at max height)
Vo = 5.79 m/s
θ = 30.1⁰
ΔX = Vxot Vy = Vyo + gt Vo = √(V xo)² + (V yo)²
ΔX
t
= Vxo Vyo = -(gt) Vo = √(5.01)² + (2.9)²
3
.59
= Vxo Vyo = - (-9.8 * .295) Vo = 5.79 m/s
5.01 m/s = Vxo Vyo = 2.9 m/s
θ = tan⁻¹( VV yo
xo
)
2.9
θ = tan⁻¹( 5.01 )
θ = 30.1⁰
Velocity and Angle at 10 meters
Vxo = 5.43 m/s
Vyo = 9.02 m/s
ΔX = 10 meters
t = 1.84 seconds (.92s at max height)
Vy = 0 m/s (at max height)
Vo = 10.53 m/s
θ = 58.95⁰
ΔX = Vxot Vy = Vyo + gt Vo = √(V xo)² + (V yo)²
ΔX
t
= Vxo Vyo = -(gt) Vo = √(5.43)² + (9.02)²
10
1.84
= Vxo Vyo = - (-9.8 * .92) Vo = 10.53 m/s
5.43 m/s = Vxo Vyo =9.02 m/s
θ = tan⁻¹( VV yo
xo
)
θ = tan⁻¹( 9.02
5.43
)
θ = 58.95⁰
Conclusion:
The catapult performed to the best of it’s ability but the marshmallow did not result in
hitting the target, although bouncing very closely outside the final ring (about 1 centimeter
away). The marshmallow was touching the rim of the cardboard target but where it landed could
not qualify as landing on the target itself. The catapult fired the marshmallow and the arch that
was made did not fly straight which caused a minor flaw in the results of the competition.
Without flying straight, the marshmallow could not have landed on the expected spot on the
large, cardboard target. This group used the equation stated in the discussion and analysis
section, y = -2.91286x + 27.9074, but after Mr.Nelson determined the distance at which the
catapult would be from the target, the x variable was replaced with the distance of 5.5 meters.
The distance in which the projectile needs to be fire in meters resembles x, that gives a y output
of how high the arm of the catapult should be off the ground in centimeters. A minor flaw in the
catapult design was using the rubber bands. Since they get stretched out, they lose tension and
slightly affect the distance traveled of the projectile. The rubber bands were placed back on the
morning of, in order to regain their strong elasticity. The tension may have been stronger than
when the catapult was tested for measurements. Therefore, there was a slight overshoot in the
first two attempts.The arm needed to be lowered to 11.9 centimeters before firing the catapult to
hit the target that was 5.5 meters away.
Works Cited:
“Characteristics of a Projectile's Trajectory.” The Physics Classroom, 2017,
www.physicsclassroom.com/class/vectors/Lesson-2/Characteristics-of-a-Projectile-s-Traj
ectory.
