On Friday the 16th in AP Physics C class, Mr. Fullerton assigned us a lab with a very simple task: shoot a ball to hit a book, if it hits the book the whole class passes, if it misses the whole class fails. Although the task seems simple, there were multiple layers to this problem, clearly with high stakes. Through this lab we were to use our skills of kinematics to determine the velocity that the instrument shoots the ball at, and then use this information to place the book at the correct location. Furthermore, we were asked to work as a class really testing out communications skills. The 22 kids in this class are some of the brightest in the school, yet our communication is where we failed.
While we should of broken up works into different groups, the whole class was all over he place sound different things, and using different values. Personally for me, my problem was trying to find the exact time of the first trial, and this prevented me from having a sufficient amount of time to do the math. Also, a problem we had when calculating the distance was using the displacement direction as a negative and the acceleration as a positive. Because the vertical displacement of he ball and the acceleration due to gravity are in the same direction, there signs should be the same. This was a vector analysis that further screwed up our final values. After making this change in the math, I was able to find the true velocity of the ball (using the equation d=(1/2)at^2+vt). With this information I could then find the distance the ball should travel with instrument set to a new angle of -4°. Using a two step kinematics problem (work attached), I was able to find the new displacement to be 1.92m in the x-direction. This value is very accurate to the actual loctation of the second firing, and if we had fixed these probaes we would not have failed.
The simple truth of it is that we did fail, as at the end of the period we were pressed with time and placed the book at a pretty random eye-balled location. It's ok for us to fail because if we analyze our failure we can learn and then chances our, we will do it right the next time!