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Projectile Motion Lab

Report

M r. M u r z a k u

N o v e m b e r 1 1 t h , 2 0 1 1

Yadesh Prashad, Timothy Yang, Saad Saleem,

Mai Wageh, Thanoja Gnanatheevam

Using a Projectile Launcher to Verify that Increasing the Initial Angle Increases the Range

Thanoja Gnanatheevam, Yadesh Prashad, Saad Saleem, Mai Wageh, and Timothy Yang.

November 7th, 2011

Abstract

We created a projectile launcher out of materials found at home. It will launch a small marble about 1.5cm in diameter. We recorded different angles to launch at, which gave us different horizontal displacements. This is to prove that by increasing the angle that we launch at; the horizontal displacement will ultimately be affected and will increase as well, until the angle reaches 45 , which gives us our maximum range. After that, the horizontal displacement decreases with the increase of the launching angle.

1 Introduction

The assignment was to create a projectile launcher to test if increasing the initial angle of an object (marble) would increase the total displacement of the launched object. The test involved launching the object and measuring the initial height, angle and the displacement of the object. By using carbon paper to accurately measure where the projectile landed, the experiment was kept precisely measured. The velocity was attempted to be kept constant throughout the experiment as well to further increase the accuracy of all measurements to reduce the error margin. The initial height was also to be kept constant. As a result of this stipulation, while altering the initial angle, the launcher’s height was adjusted so that the release point (the exit point of the object from launcher) remained the same. This, again, further increased the accuracy of the overall experiment.

As the experiment was conducted as accurately as possible, the variables that affected the result included:

 The initial angle (Ѳi)  The initial height (dy)  The size (mass) of the projectile  The size of the launcher  The initial velocity (Vi)  Acceleration (gravity) (g)

2 Theory

The purpose of the experiment was to prove or disprove that if the initial angle was increased to a certain degree, the maximum displacement would be achieved. By existing knowledge, the angle that would achieve the maximum height of a projectile would be 45 degrees.

Using the equations,

3 Data

Δdy Δdx θi vi

m

m 0°

m/s

m

m 30°

m/s

m

m 45°

m/s

m

m 55°

m/s

m

m 70°

m/s

The initial angle effects the displacement of the projectile

The initial height of the launcher effects the total displacement of the projectile

Depending on how far back the balloon is stretched changes the initial velocity

This graph conclusively proves that as the initial angle of the projectile increases, the ranges also exponentially increases until the angle reaches 45 degrees. After that, as the angle increases the range decreases exponentially, verifying that 45 degrees provides the maximum range. The error bars represent the human error of reading measurements and different launch techniques.

4 Conclusion

Through this experiment, our hypothesis has been verified. It was confirmed as the marble was

launched furthest at 45 degrees. It validated that as the angle increased up to 45 degrees, the

horizontal displacement increased as well. As the angle increased beyond 45 degrees, the horizontal displacement decreased. The theory was formed based on prior knowledge on the physics of projectile

motion. The experiment was conducted with great caution in attempt to achieve the most accurate

results possible. To ensure precise results, carbon paper was utilized to keep track of the marble's

landings, a protractor was used to measure initial angles and rulers were used to measure horizontal

displacements, initial height, as well as the initial velocity.