Angle that yielded best results: 42º (393cm on average)
Data Processing + Presentation
Using my results, notably the average distance achieved for the given angle projections, I created a graph from which we can deduce the angle of projection that will hive the largest range.
On the following page you will find the graph of the data with the given errors and uncertainties taken into account. On the graph I have plotted the different angles against the distances achieved at those angles by the rubber band
By observing the graph, it is clear that there is an increasing trend between 5 and 40 degrees. In other words, as the angle of projection increased, so did the range of the bad, although not at proportional rates. Moreover, we can see that after the 42-45 degree mark, the line experiences a downwards decreasing trend. From this I can deduce that the angle of projection that will give the largest range is certainly between 40 and 45 degrees, and to be more precise it appears to be at 42 degrees.
Conclusion and Evaluation
From the experiment I conclude that indeed, the range of a projectile does depend on the angle at which it is projected. Moreover, up until around 40-50 degrees, the range increases as the angle increases whereas after that point it is likely to decrease. From theory it is known that the ideal angle to fire a projectile if aiming for maximum range is 45 degrees, and this has been proved mathematically and experimentally. Our value of 42 degrees is not entirely correct but is nonetheless close to the literal value of 45.
Evaluating procedures and results
One of the greater weaknesses in this experiment was the failure to obtain a more accurate measuring device for the angle of projection. Although the inclined plane we used gave degrees correct to the nearest degree, it was often hard to read and the marker was too thick. Although not that significant in the long run, when we concluded that the maximum range is obtained by firing somewhere between 40 and 50 degrees, it was vital to have more accurate measurements because the difference between the two is so great. Other weaknesses in the procedure include the inability to always launch the rubber bands in the exact same manner for all trials. Although we did our best to expand the band to the same distance each time, the nature of the rubber band is such that you can not duplicate the same procedure over n over again without minor differences. Of course one must not forget about the exogenous factors that had impact on our experiment. I noticed during the procedures that a window was open in the laboratory. Any incoming wind could have resulted in air interference and affected several trails. This could cause some rubber bands to fly further, closer, or even go off balance. Another obvious limitation of error that we unfortunately encountered was the inability to create an angle greater than 50 degrees. This was a shame because we could not rule out that there are no angles beyond 50 that would yield greater ranges than 42 degrees, although our line graph suggested it. Moreover, due to the nature of the rubber band, the place where it made impact with the floor and the place where it finally landed differed greatly. Since each time the band would bounce off differently, we had to keep one member of the group as an observer to measure where the band initially makes impact. Since this all happened so quick and our eyes are only as accurate as we can see, it could have caused several errors.
Improving the investigation
Were we to repeat an experiment of a similar nature over again, there are several changes I would implement to limit the weaknesses. Firstly, by using a marble or some sort of more dense and inelastic material you minimize interference from the wind greatly. Although it is true that you cannot project a marble simply with an incline plane like we did with the rubber band, but some sort of projection gun device could be obtained. Another realistic suggestion would be to use a protractor instead of trusting the markers on the incline plane. I believe this would slightly increase the accuracy since the protractors are pretty clear.