Purpose
The purpose of this lab is to find how far a projectile is fired, it's velocity, and time it took.
Theory
We are able to predict how far the projectile will be fired and the time it will take by first measuring the initial velocity. The first step is to derive the 3rd kinematic equation of projectile motion.
0 = t(Voy - 1/2gt)
0=Voy-1/2gt
t=2voy/g
This equation is then put into the range equation
R=Voxt
R=Vox(2voy/g)
0=Voy-1/2gt
t=2voy/g
This equation is then put into the range equation
R=Voxt
R=Vox(2voy/g)
Experimental Technique
I had to set the launcher at an angle of 30 degrees before launching the ball.
The shots were a few centimeters off of where i predicted it to be and they are all fairly close to each other.
Data and Analysis
Equations:
I first found the velocity to be 3.92m/s, so then I was able to find Voy and Vox
Sinθ=Voy/3.92m/s
Voy=3.92m/sSin35
Voy=2.25m/s
Cosθ=Vox/3.92m/s
Vox=3.92Cos35
Vox=3.21m/s
Then I can solve for time with
1/2gt=Voy
gt=2voy
t=2Voy/g
t=2.25m/s(2)/9.8m/s^2
t=0.46s
R=Voxt
R=3.21m/s(.46s)
R=1.47m
I first found the velocity to be 3.92m/s, so then I was able to find Voy and Vox
Sinθ=Voy/3.92m/s
Voy=3.92m/sSin35
Voy=2.25m/s
Cosθ=Vox/3.92m/s
Vox=3.92Cos35
Vox=3.21m/s
Then I can solve for time with
1/2gt=Voy
gt=2voy
t=2Voy/g
t=2.25m/s(2)/9.8m/s^2
t=0.46s
R=Voxt
R=3.21m/s(.46s)
R=1.47m
Conclusion
Overall, I was able to accomplish the task of finding out the distance, time, and velocity of a projectile shot from a launcher. My projectile shot 1.47m in 0.46s at 3.92m/s. The uncertainty of the range measurement is + or - one centimeter. My predicted measurement was within 2.3 cm of the actual measurement, which was fairly close. Some of this error might of been caused by inaccurate measurements and slight movements of the paper when trying to place it on the floor. Also this could of been cause by placing the plumb bob in the wrong spot and measuring from the wrong spot. The distance might of been affected slightly by how fast I pulled the string of the launcher. When the string is pulled faster the projectile will go slightly further. I think that wind resistance was not a factor since the projectile was small and dense enough to not have air affect it. Also, since we were inside, there was no wind to affect the outcome.
References
Boyle, Joseph J., and Douglas C. Giancoli. Study Guide: Physics, Principles with Applications, Fifth Edition. Englewood Cliffs, N.J.: Prentice Hall, 1998. Print.