Author: Zach Christoff
Lab Partner: Daniel Baka
Date: 10/20/15
Lab Partner: Daniel Baka
Date: 10/20/15
Purpose
We will investigate projectile motion by finding the initial velocity of a ball shot from a launcher. We will also predict the range of the launch by deriving an equation.
Theory
This is a representation of how our projectile will be launched. In theory, where the ball lands on the floor should be equal to the range we calculated using the following equations:
I solved for t by using the quadratic equation. Once t was solved for, I swapped variables for their derivations so I had all the information necessary to plug in to their respective variable.
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All that was done in this step was swapping variables for their derivations. Since we didn't know initial velocity in the x direction, I substituted in the equation that is equal to initial velocity in the x direction. The same applies for t (time).
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Experimental Technique
4.) A measuring paper and carbon paper was placed 3.90 meters away from the launcher. The projectile was then shot 10 times, and the carbon paper left a mark on the measuring paper. After the 10 shots were recorded, I measured the distance of each individual shot and averaged the ranges. The average range ended up being 3.8889 meters versus the predicted range of 3.90 meters.
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Data
Analysis
Conclusion
The uncertainty in the range measurement is +/- 0.0244 m, as shown in the analysis. My predicted and measured range are not very far apart. The difference between the two was only 0.0111 m, or a percent difference of 0.2846%. My projectile launcher was fairly consistent, which allowed for the predicted and measured range to match up pretty closely. For each range measurement, there is some parallax error, which I tried to eliminate by looking directly above the measuring tape. Additionally, I measured my launch at an angle of 40 degrees. The launcher was most likely not set at exactly 40 degrees when I measured initial velocity and the 10 shots because it was adjusted multiple times in between. I do think wind resistance played a factor in the measurements because many shots were consistent, but a few were further off than others. The launchers aren't always perfectly consistent, but wind resistance can definitely play a part. The projectiles that were used are not the heaviest of objects, which allows the air to act on them and add a bit of resistance. If we were in a closed-off room with no movement or draft, then I would say wind resistance played no factor, but that was not the case.
References
Giancoli, Douglas C. Physics: Principles with Applications. 5th ed. Upper Saddle River, N.J.: Prentice Hall, 1998. Print.