Projectile Motion
Purpose:
An object in a projectile motion move horizontally with no acceleration and vertically with the gravitational acceleration at the same time. This experiment is to investigate projectile motion using experiments, equations and comparing the expected and experimental data. Procedure:

Case I:
Use formulas to find equation of horizontal Range (R) in a projectile motion. Rearrange equation for Rmax, and find the angle
Adjust the launches angle to angle
Launch the ball, measure Rmax
Use the equation to solve for initial speed
Case II:
Calculate new R=80/100Rmax
Use to calculate ()
Find out another expected angle , and find its relation with Adjust the launch angle to , launch the ball and measure R
Adjust the launch angle to , launch the ball and measure R
Compare R1 and R2 with R
More Calculation:
Calculate components of velocity for both cases using expected value Calculate maximum height for case I only
Data and Calculations:
In Projectile Motion:
Horizontally (x-direction)：
a=0, v=V, X=vt,
Vertically (y-direction):
a=-g, y=vt-1/2gt
Also, v=vcos, v=vsin
We can get R=
Case I:
As -1≤sin2≤1, so sin(2)max=1, so Rmax=v/g, and =45
When the launch angle is 45， Rmax from experiment we get was 1.75m Using equation, we can calculate for V==4.14m/s
Case II:
R=80/100Rmax=1.4m
As, R=, SO expected values of are , and
When the launch angle is 26.6, the range we get R=1.45m;
When the launch angle is 63.4, the range we get R=1.35m.
They are both around the expected range which is R=1.4m
More Calculation:
Components of velocity
For case I:
V=Vcos45=2.93m/s,
V=Vsin45=2.93m/s
For case II:
When angle is 26.6, v=Vcos26.6=3.7, V=Vsin26.6=1.85 m/s When angle is 63.4, v=Vcos63.4=1.85, V=Vsin63.4=3.7m/s Maximum height for case I
Rmax=Vt, t= Rmax/V = 1.75/2.93=0.597s
Hmax=V(t/2)-1/2g(t/2)=2.93*(0.597/2)-1/2*9.81*(0.597/2)=0.438m Conclusion:
For case one, we...

...Lab II, Problem 3:
ProjectileMotion and Velocity
Oct. 06, 2013
Physics 1301W, Professor: Hanany, TA: Vladimir
Abstract
A ball is tossed obliquely. The vectors of position and velocity are measured.
The acceleration is calculated.
Introduction
A toy company is now making an instructional videotape on how to predict the position. Therefore, in order to make the prediction accurate, how the horizontal and vertical components of a ball’s position as it flies through the air should be understood. This experiment is to calculate functions to represent the horizontal and vertical positions of a ball. It does so by measuring and calculating the components of the position and velocity of the ball during the toss. Therefore, we can also calculate the acceleration during the procedure.
Prediction
The x-axis is located on the ground level horizontally, pointing to where the ball is initially thrown, that is opposite the direction the ball flies. The vertical y-axis passes through the highest point of the ball during the fly and point upward.
Since the ball experiences no other force, except for gravity, during the toss. There is no horizontal force. It is predicted that the ball should have a constant horizontal speed, which is the horizontal component of initial velocity. Vertically, it has gravity pulling it down all the time. So it should have an acceleration of –g (minus is for the direction). Since it has a...

...Abstract
In this lab experiment the range equation will be used to calculate range of the launched rocket, initial velocity and distance traveled. Various projectiles will be tested at various angles and table heights for experiment one. Results will be compared to initial calculations. Despite human error and calculation error, the results still correlated with the hypothesis.
Introduction
Background
Acceleration is constant at 9.8 m/s2 because of the force of gravity. For experiment 1 the velocity will be calculated by measuring “x” and “y” and using the combined x & y equations to solve for Vo. Vo= x⌠g/2y. For experiment 2 the range equation for distance x=R is applicable since the launch and landing elevations are the same. R=(Vo2sin2ᶿ)/g
Objective
The objective of experiment one is to determine the distance a falling object will travel when the launch height is changed. The objective of experiment two is to observe the distance, x=R, a projectile will travel when the launch angle is changed. Acceleration is constant at 9.8 m/s2 in all the experiments due to gravity.
Hypothesis
Experiment 1: When the height is raised, the marble will have more time to continue traveling at its initial velocity while the gravitational force is acting upon it, increasing the distance the marble travels while falling.
Experiment 2: The range of the rocket will decrease as the angle launched moves away from 45 degrees.
Experiment...

...
Conclusion:
One source of error comes from when we shot the cannon from the ground at a 45° incline. There is a little drop off at the end of the range because the height at which the ball is being shot is a little above ground. This could have an effect on measuring the correct distance.
Also, we did not have measuring tape for measuring distance. We had to use multiple meter sticks to measure the distance. After sticking the meter sticks together to get a long range, this could easily throw off your calculations for distance.
With all the formulas involved, it is possible to type a wrong number into the calculator.
I believe our calculations for velocity and distance from the trials at different angles give a good picture projectilemotion. If a ball is shot up in the air at an angle 45°, it has a greater distance and velocity than a ball that is being shot horizontally at 0°....

...Example ProjectileMotionLabReport
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 labreport, 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...

...ProjectileMotion
You have probably watched a ball roll off a table and strike the floor. What determines where it will land? Could you predict where it will land? In this experiment, you will roll a ball down a ramp and determine the ball’s velocity with a pair of Photogates. You will use this information and your knowledge of physics to predict where the ball will land when it hits the floor.
[pic]
Figure 1
objectives
* 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.
* Take into account trial-to-trial variations in the velocity measurement when calculating the impact point.
Materials
|POWER MACINTOSH OR WINDOWS PC |PLUMB BOB |
|LABPRO OR UNIVERSAL LAB INTERFACE |RAMP |
|LOGGER PRO |TWO RING STANDS |
|TWO VERNIER PHOTOGATES |TWO RIGHT-ANGLE CLAMPS |
|BALL (1- TO 5-CM DIAMETER) |METER STICK OR METRIC...

...initial horizontal velocity of the soccer ball.
Problem Type 2:
A projectile is launched at an angle to the horizontal and rises upwards to a peak while moving horizontally. Upon reaching the peak, the projectile falls with a motion that is symmetrical to its path upwards to the peak. Predictable unknowns include the time of flight, the horizontal range, and the height of the projectile when it is at its peak.
Examples of this type of problem are
a. A football is kicked with an initial velocity of 25 m/s at an angle of 45-degrees with the horizontal. Determine the time of flight, the horizontal distance, and the peak height of the football.
b. A long jumper leaves the ground with an initial velocity of 12 m/s at an angle of 28-degrees above the horizontal. Determine the time of flight, the horizontal distance, and the peak height of the long-jumper.
The second problem type will be the subject of the next part of Lesson 2. In this part of Lesson 2, we will focus on the first type of problem - sometimes referred to as horizontally launched projectile problems. Three common kinematic equations that will be used for both type of problems include the following:
Equations for the Horizontal Motion of a Projectile
The above equations work well for motion in one-dimension, but a projectile is usually moving in two dimensions -...

...
Lab 4 ProjectileMotion
Sai Moua
Purpose: The purpose of this lab was to define what the initial velocity of the ball when it is launched out of the pipe. Our next objective is to determine at what angle that the ball will be ejected at the maximum range. Lastly, we predict and confirm the range before we launch the ball at a certain angle.
Theory: Projectilemotion according to Dr. James S. Walker is defined as, “the motion of objects that are initially launched –or “projected”- and that then continue moving under the influence of gravity alone” (82). Gravity is the lone force acting on the projectile when in motion. There are two components to a velocity vector. The horizontal velocity component is the effect it has on moving the projectile horizontally. On the other hand the vertical component affects the velocity by moving the projectile vertically.
Procedure: To begin the lab set the launcher to a medium range setting. We used carbon paper on top of white paper to determine where the ball lands on the floor. We then shot the ball at angles of 30, 35, 40, 45, and 50 degrees. We recorded the distances after each shot and determined that shooting the ball at 40 degrees gave us the maximum range. We kept the launcher at a medium setting and shot the ball straight out 5 times and...

...Title
ProjectileMotion
Abstract
A projectile was fired from atop an elevation and an angle. The initial velocity for each
firing was likely to be the same. The distance traveled in the horizontal direction was measured
for multiple firings of each trial, and the values were averaged. When the initial velocity for
each of these averages was calculated it was proved that the initial velocity was relatively
constant. These measurements had many possible sources of error including air resistance and
firing position. This lab increased understanding of projectilemotion.
Introduction
Projectilemotion occurs when an object in a two dimensional plane experiences motion
only due to gravity. Kinematic equations can be used to describe the components of projectilemotion. This allows us to analyze the motion. In this lab measurements will be taken to
determine the initial velocity of objects experiencing projectilemotion. This will first be done
for objects that are starting from a set elevation above the landing area. Then the initial velocity
will be found for objects that are launched from the floor at an angle to a landing area of the ...