Determining the Maximum Distance Travelled Using Projectile Motion

November 05, 2012

Faustin Combe
Alex Gazso
Maria Henriquez

Abstract:
This experiment determined the maximum distance a projectile can travel in the best angle range by shooting a projectile at various angles then measuring the distance travelled. This experiment used a toy gun, Nerf N-Strike Jolt Ex-1, which was attached to a wooden structure with a u-hook suspension and protractor. The toy gun was shot in variety of angles, afterward; measuring the distance it travelled from the wooden structure to the place it dropped.

Introduction:
A “projectile” is defined as an object subject only to the force of gravity and no other forces. For example, arrows, darts, and bullets are considered projectiles. Parabolic motion has been studied for a long time dating all the way back to the time in which Galileo was conducting experiments. He accurately described projectile motion as objects in motion through air in two dimensions near the earth’s surface. The purpose of this experiment is to determine the best angle measurement that covers the farthest distance by shooting a projectile in different angles. The method used to determine the maximum distance travelled is using a wood structure with a u-hook suspension attached with a protractor and a Nerf N-Strike Jolt Ex-1. The wooden structure holds the Nerf gun in various angles, therefore allowing the nerf bullet to be shot in a desired angle. If one wishes to know which angle allows maximum distance travelled, shooting a nerf gun at a certain angle is a reliable method. Determining the angle that allows maximum distance travelled is significant to examining general motions of objects in the world in two dimensions such as kick or thrown footballs and. An angle of 65 degrees will allow the nerf bullet to travel the maximum distance. Materials:

Wood structure with a u-hook suspension
Meter stick
Nerf N-Strike Jolt Ex-1
Protractor...

...ProjectileMotion
Experiment # 4
Introduction:
ProjectileMotion exists commonly in our everyday lives and is particularly evident in the motion or flight of objects which are projected from a particular height. The key to working with projectilemotion is recognizing that when an object with mass is flying through the air, its motion is a combination of vertical and horizontal movements. Although the horizontal velocity of the object remains constant throughout the flight, it’s vertical velocity accelerates or decelerates due to gravity.
Purpose:
The purpose of this experiment is to be able to measure the velocity of a ball using two Photogates and computer software for timing, apply concepts from two-dimensional kinematics to predict the impact point of a ball in projectilemotion and ability to understand trial-to-trial variations in the velocity measurement when calculating the impact point.
Materials:
Computer plumb bob
Vernier computer interface ramp
Logger Pro two ring stands
Two Vernier Photogates two right-angle clamps
Ball(1 to 5 cm diameter) meter stick or metric measuring tape
Masking tape target
Procedure:
1) Set up a low ramp made of...

...Lebanese American University
Classical Physics
3 . ProjectileMotion
Objectives:
Students will measure the maximum height H and the range R of a projectilemotion.
They will study the effect of the shooting angle on H and R.
Material used:
4 rulers, track, metallic ball, landing track, A4 white paper, red carbon paper, timer + supply, gun
+ protractor.
Theory:
A projectile is an object upon which the only force acting is gravity. There are a variety
of examples of projectiles: an object dropped from rest is a projectile (provided that the
influence of air resistance is negligible), an object thrown vertically upwards is a
projectile (provided that the influence of air resistance is negligible), and an object
thrown upwards at an angle is also a projectile (the same assumption). A projectile is
any object, which once projected, continues its motion by its own inertia and is
influenced only by the downward force of gravity.
By definition, a projectile has only one force acting upon - the force of gravity. If there
were any other force acting upon an object, then that object would not be a projectile.
Projectiles can be launched both horizontally and vertically, and they have both
horizontal and vertical velocity and horizontal and vertical displacement.1
...

...investigation By Rex Whiticker
ProjectileMotion
Abstract:
The Project motion of a catapult being fired is varied by a range of factors that affect the path of the projectile. In this experiment, the angle of trajectory, mass of the projectile and change in initial velocity of the launch, were all factors considered in the end result to investigate the properties of projectilemotion. The purpose of the experiment was to conduct a first-hand investigation to design and analysis how angle, weight and power affect projectilemotion, collecting approximate values and recording results.
Introduction:
Parabolic motion has been studied for a long time dating all the way back to the time in which Galileo was conducting experiments. During the experiment two angles were fired at 320 and 100 at two different power levels and weights.
Galileo was the first person who accurately described projectilemotion. Because of the drawings of Niccolo Tartaglia, Galileo realized that a projectile followed a curved path which is called a parabola. The parabola had an exact mathematical shape that was acted upon two forces, vertical and horizontal. His experiments included rolling balls down a highly polished inclined plane (to lower the acceleration) and record similarities. His work showed that...

...Name: Lab Group 4
Date: 10/26/2011
Partners: Kayla Stephens, Robin Poole, Megan McIlvoy
Grade:
Instructor: JPS
Name: Lab Group 4
Date: 10/26/2011
Partners: Kayla Stephens, Robin Poole, Megan McIlvoy
Grade:
Instructor: JPS
Physics I Laboratory Worksheet
Lab 4: ProjectileMotion
Objectives: Using a projectile gun on an incline plane, calculate the
velocity of the steel ball at ten different distances, then find the average
velocity. In order to find the velocity of the steel ball two different
equations are needed. In order to find the velocity of the steel ball fired
from the projectile gun on an inclined plane, the first equation must be
manipulated and substituted into the second equation. Then use the average
velocity to determine the distance of a projectile being released at a different angle.
Physics Principles:
* Converting from centimeters to meters
* Trigonometric functions
* Quadratic formula:x=-b±b2-4ac2a
* Know how to get the derived formula:
Materials Needed:
* Projectile gun
* Projectile
* Incline paper
* Carbon paper
* 4 sheets of regular printing paper
* Tape Measure
* Calculator
* Pen
* Notebook paper
Pre-Lab exercise: Using the two formulas solve forv0.
Equation 1: x= v0xt(vox=v0cosθ)
x=v0cosθ(t)
t=xv0cosθ
Equation 2: y= y0+v0yt-12gt2(v0y=v0sinθ)
y=...

...Example ProjectileMotion Lab Report
You may not copy the exact words here in any way on a re-written lab.
Determination on the Effect of Angle on the Range of a Projectile
Joselyn J. Todd, other science students, and even other science students
Sept. 12, 2006
Joselyn J. Todd, Example Lab, 9/12/2006
2
Introduction
Parabolic motion has been studied for a long time dating all the way back to the
time in which Galileo was conducting experiments. In this lab report, the range a
foam disk launcher shot was tested by altering the angle of trajectory followed by
measuring the range. The range that the foam disk went was measured in
centimeters and multiple shots were taken at each angle and then averaged.
Galileo was the first person who accurately described projectilemotion. Because
of the drawings of Niccolo Tartaglia, Galileo realized that a projectile followed a
curved path which is called a parabola.1 It was later found out by Galileo that the
parabola has an exact mathematical shape. Also, he stated that a projectile was
acted upon by two forces, vertical and horizontal. The vertical force was from
gravity, which pulled it to Earth at 9.8 m/s. That is why a parabola is a precise
mathematical equation.2
Observations were conducted before the experiment was started. First,
observations were made on two racquetballs, one being...

...
ProjectileMotion
Objectives:
The purpose of this experiment is to examine the projectilemotion of a ball launched horizontally. The initial velocity will be calculated. The range of the ball will be measured.
Theory:
Horizontal launch of the ball allows computing the initial velocity v0 by measuring the height of the launch and the distance traveled by the ball:
h=, s=v0 ∙ t
Solving these parametric equations for v0 gives us:
0=s
Where h and s are defined from the experiment
Equipment:
*projectile launcher and plastic ball
*carbon paper
*white paper
*meter stick
*tape
*stand with a clamp
Procedures:
1. We set up the projectile horizontal position.
2. We measured for the height at which the ball will be launched. h=0.310m
3. We put the plastic ball into the projectile launcher and charged it for the short range launch.
4. We made a test shot to determine the position of a sheet of white paper covered with a carbon paper.
5. We taped the sheet of white paper to the area of a ball landing.
6. We made five shots of the ball.
7. We measured the distance (range) of the ball motion on each trial, and the height it was launched from.
8. We calculated the initial velocity v0 for each trial.
All the obtained data has been recorded in the Table below.
Height, h (m)
Distance, s (m)
Velocity, 0 ()
Average...

...TITLE
To investigate the trajectory of a small ball as it rolls off a surface which is inclined to the horizontal.
OBJECTIVE
To investigate the trajectory of a two dimensional motion
APPARATUS & MATERIALS
Ramp
Wooden block
Pendulum bob
Plumb line
Steel ball
Wooden board
Carbon paper
Meter rule
Plasticine
SETUP
1. A ramp has been set up at the edge of a bench as shown in the Figure 4-1.
2. Suspend a plum-line from the edge of the bench as shown in Figure 4-2.
3. Mount a wooden board horizontally using two clamps so that the board is situated
about the bottom of the ramp.
4. Place a sheet of blank paper on top of the board.
5. Place a piece of carbon paper on the top of the blank paper. The ink-side of the
carbon paper should be facing down.
6. When a ball is released at the top of the ramp, the ball will travel through a
trajectory as shown in Figure 4-2.
THEORY
Let:
g =
u = speed of the ball as it leaves the ramp
k = constant
y = vertical distance (between the bottom of the ramp and the top of the board)
x = horizontal distance (between the plum-line and mark on the paper)
The equation which relates to x and y is
PROCEDURE
1. Position the ball at the top of the ramp. Release the ball so that it rolls down the
ramp and onto the board below.
2. Remove the carbon paper and observe that the ball makes a small mark on the blank
paper....

...ProjectileMotion
The purpose of this lab is to study the properties of projectilemotion. From the motion of a steel ball projected horizontally, the initial velocity of the ball can be determined from the measured range. For a given initial velocity, the projectile range will be measured for various initial angles, and also calculated by applying the theory for motion with constant acceleration. For further background information, refer to the sections in your textbook on projectilemotion and motion with constant acceleration.
THEORY For a given initial velocity, v0 , and initial position, s0 ,the position of a particle, s, as a function
of time, undergoing constant acceleration, a is given by sr = sr 0 + vr 0 t + 12 ar t 2 ( 1 )
This is a vector equation and can be broken up into its x, y, and z components. Since the motion is in a plane, we need only look at the x and y components. If we neglect air resistance, the acceleration in the y direction is -g, due to gravity. The acceleration in the x direction is zero. Hence, the vector equation (1) becomes two scalar equations:
If we eliminate t in Eqs.(5) we get y as a function of x. gx2
and solving for vo we get
x = x0 + v 0x t (2) y=y+v t-1gt2
0 0y In terms of the angle θ, and the initial speed vo, the initial velocity components are
v0x=v0cosθand v0y=v0sinθ...