Experiment
In this experiment, along with my partner Dakota Smith, we predicted the range of metal balls fired from spring-loaded cannons. Each of us used a different power and angle, therefore ensuring different results amongst the group. To find these results, we used pre-determined values from firing the cannon and used them to find the other values (equations used below in work).
Theory
Following the pre-requisites states above, we each went about doing our own experiment. To achieve our goal, we used data from our individual launches along with math acquired through the use of kinematics, mainly using the five kinematic equations for horizontal and vertical motion (seen above). We also used values to our knowledge, such as vertical acceleration being downward of gravity.
Experimental Technique
To begin my experiment, I took ten shots from the cannon at the specified power setting and angle, where the average velocity of those shots (5.446 m/s, in this case) to give me the value for true velocity. Having the angle of 60° and one "side" of the velocities, I was able to use SOHCAHTOA to find the values of horizontal and initial vertical velocity. Afterwards, I measured the height from table to ground (Δy) in order to use the kinematic equations to find the value of the range. However, to do this, I have to derive multiple equations to find one to match the current values I know.
By finding this equation, I was then able to plug in the known variables and remove any unknown values in order to find the range of the shot, which was 304.382 cm. After finding this, I then went back to see if this value was correct by launching and measuring the cannon using the same settings as before. Finally, after averaging the points where the ball hit the carbon paper, I used the average of those shots and the derived value I found in order to find the error in the answers. Going through the math for % error, I come to around a 0.946% error in my answers from the mathematical and ten-shot finalization.
Analysis
Judging by how the experiment went, most of it was largely a success. However, every experiment comes with its own share of inaccuracies, and this one is no exception. Many of the shots taken the second time were shifted over to the left of the where it should have landed. This was most likely caused by problems with the cannon itself, which can not be helped and unfortunately affected the data. Even though this inaccuracy, along with any caused by rounding and the use of estimated values in the mathematics, the data was not too affected, and the answer acquired was still close to actual value, making the experiment a success. To better conduct the experiment next time, the only thing I would like to have is an accurate cannon, due to a bit of perfectionism.
Conclusion
Even though alot of things went wrong, whether they be in the experiment itself of just trying to get this bloody page up and functional, I believe that this was overall a success. Though painful in many aspects, and certain little things arose that could not be controlled such as the cannon's trajectory and mathematical inconsistencies, the ball landed close to the the landing point and was considerably accurate.