## Lab Practicum - Buggy Projectile Launch Lab Rich Text Content

Procedure

In this lab, one will lay 2 meter sticks end to end and run the buggy along said meter sticks using a hand-held stopwatch to track how long it takes (in seconds) for the toy buggy to travel 2 meters. Repeat the following step for five trials. Using this information, one can determine the velocity of the toy buggy. Next, using a meter stick, one will measure the height above the ground that the muzzle of the projectile launcher lies. Using the same equipment, measure the height above the surface that the top of the toy buggy lies. Set the angle of the projectile launcher to 0 degrees (otherwise known as a horizontal launch angle) and set the launcher to medium range. Feed the ball into the projectile launcher and launch the yellow ball off of the tabletop to land on carbon paper, which should be taped carbon face down on top of a piece of paper that is taped to the ground. Measure the horizontal distance between where the yellow ball hits the ground, marked by the blue dot on the paper, and the muzzle of the projectile launcher using several meter sticks. Repeat the following three steps for ten trials. Using this information, one can calculate the muzzle velocity of the projectile launcher.

Data Table - Buggy #e, Launcher #e

 Time (in s) for buggy to travel 2m (+/- 0.01s) Height (in m) of muzzle of projectile launcher (+/- 0.001m) Height (in m) of top of surface of buggy (+/- 0.001m) Horizontal distance (in m) between muzzle and where yellow ball hits ground (+/- 0.001m) Trial 1 4.38 s 1.184 m 0.072 m 2.234 m Trial 2 4.49 s n.a. n.a. 2.212 m Trial 3 4.44 s n.a. n.a. 2.235 m Trial 4 4.43 s n.a. n.a. 2.237 m Trial 5 4.46 s n.a. n.a. 2.284 m Trial 6 n.a. n.a. n.a. 2.213 m Trial 7 n.a. n.a. n.a. 2.226 m Trial 8 n.a. n.a. n.a. 2.209 m Trial 9 n.a. n.a. n.a. 2.237 m Trial 10 n.a. n.a. n.a. 2.262 m

Calculations

Average Horizonal Distance Traveled by Ball = 22.349 +/- 0.010 m / 10 = 2.235 +/- 0.001 m

y = y(initial) + v(initial)*t + 1/2*a*t^2

0 = 1.184 +/- 0.001 m + 0 * t + 1/2 (-9.8 m/s^2) * t^2

t^2 = 1.184 +/- 0.001 m / 4.9 m/s^2

t = 0.4916 +/- 0.002 s

v(muzzle) = x(avg.) / t = 2.235 +/- 0.001 m / 0.4916 +/- 0.002 s = 4.456 +/- 0.004 m/s

Average Time for Buggy to travel 2 m: (22.20 +/- 0.05 s) / 5 = 4.44 +/- 0.01 s

v(buggy) = x / t(avg.) = 2 m / 4.44 +/- 0.01 s = 0.450 +/- 0.001 m/s

1.184 +/- 0.001 m - 0.072 +/- 0.001 m = 1.112 +/- 0.002 m

t(buggy) = 3 m / 0.450 +/- 0.001 m/s = 6.67 +/- 0.02 s

Explanation of Computational Model

Using the information calculated above and the computational model in class, we plugged in v(muzzle) as 4.456 m/s and the initial position of the projectile as 1.112 m. We started our first test at theta = 45 degrees, but that was too far, so we decreased the value by 0.5 degrees until the ball hit the mark at 3 m distance. This occurred at the 30.5 degree mark. We recorded the output of the time for the projectile to land 3m away and we subtracted that number from 6.67 +/- 0.002 s to get the delay between the launch of the buggy and the launch of the projectile. We set the angle of the launcher at 30.5 degrees and, after waiting for the time delay that we calculated, fired the projectile.

Results and Reflection

My group hit the buggy at 3m. Yay! :D

This lab was a really great lab for a variety of reasons, but mainly because it struck a happy medium between last year and the rest of my physics career. Though it offered some hints of Honors Physics types of problems (same model used), its complexity made it an interesting exercise, at least for me. I learned through completing this lab that I should avoid algebra whenever possibly, a thought that probably all of my math teachers would scoff at. After spending countless hours attempting to find an algebraic solution to the problem without use of a calculator, I eventually just plugged the equation into my calculator to find theta, but even that was time consuming. When the computational modeling was introduced for this unit, I really like the flexibility it offered, its ease of use, as well as the speed at which one could arrive at a solution. I also liked knowing the time that it took for the projectile to complete its path, without having to crunch numbers endlessly. In the future, I will continue to use computational modeling to broaden my understanding of physics concepts, as well as to conceptualize difficult ideas.

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